1
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Potratzki M, Bröhl T, Rings T, Lehnertz K. Synchronization dynamics of phase oscillators on power grid models. CHAOS (WOODBURY, N.Y.) 2024; 34:043131. [PMID: 38598675 DOI: 10.1063/5.0197930] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Accepted: 03/25/2024] [Indexed: 04/12/2024]
Abstract
We investigate topological and spectral properties of models of European and US-American power grids and of paradigmatic network models as well as their implications for the synchronization dynamics of phase oscillators with heterogeneous natural frequencies. We employ the complex-valued order parameter-a widely used indicator for phase ordering-to assess the synchronization dynamics and observe the order parameter to exhibit either constant or periodic or non-periodic, possibly chaotic temporal evolutions for a given coupling strength but depending on initial conditions and the systems' disorder. Interestingly, both topological and spectral characteristics of the power grids point to a diminished capability of these networks to support a temporarily stable synchronization dynamics. We find non-trivial commonalities between the synchronization dynamics of oscillators on seemingly opposing topologies.
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Affiliation(s)
- Max Potratzki
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany
| | - Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
- Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany
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2
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Chinichian N, Lindner M, Yanchuk S, Schwalger T, Schöll E, Berner R. Modeling brain network flexibility in networks of coupled oscillators: a feasibility study. Sci Rep 2024; 14:5713. [PMID: 38459077 PMCID: PMC10923875 DOI: 10.1038/s41598-024-55753-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 02/27/2024] [Indexed: 03/10/2024] Open
Abstract
Modeling the functionality of the human brain is a major goal in neuroscience for which many powerful methodologies have been developed over the last decade. The impact of working memory and the associated brain regions on the brain dynamics is of particular interest due to their connection with many functions and malfunctions in the brain. In this context, the concept of brain flexibility has been developed for the characterization of brain functionality. We discuss emergence of brain flexibility that is commonly measured by the identification of changes in the cluster structure of co-active brain regions. We provide evidence that brain flexibility can be modeled by a system of coupled FitzHugh-Nagumo oscillators where the network structure is obtained from human brain Diffusion Tensor Imaging (DTI). Additionally, we propose a straightforward and computationally efficient alternative macroscopic measure, which is derived from the Pearson distance of functional brain matrices. This metric exhibits similarities to the established patterns of brain template flexibility that have been observed in prior investigations. Furthermore, we explore the significance of the brain's network structure and the strength of connections between network nodes or brain regions associated with working memory in the observation of patterns in networks flexibility. This work enriches our understanding of the interplay between the structure and function of dynamic brain networks and proposes a modeling strategy to study brain flexibility.
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Affiliation(s)
- Narges Chinichian
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany.
- Psychiatry Department, Charité-Universitätsmedizin, Berlin, Germany.
- Bernstein Center for Computational Neuroscience, Berlin, Germany.
| | - Michael Lindner
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
- Potsdam Institute for Climate Impact Research, Potsdam, Germany
| | - Serhiy Yanchuk
- Potsdam Institute for Climate Impact Research, Potsdam, Germany
- Institute of Mathematics, Humboldt Universität zu Berlin, Berlin, Germany
- School of Mathematical Sciences, University College Cork, Cork, Ireland
| | - Tilo Schwalger
- Bernstein Center for Computational Neuroscience, Berlin, Germany
- Institute of Mathematics, Technische Universität Berlin, Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience, Berlin, Germany
- Potsdam Institute for Climate Impact Research, Potsdam, Germany
| | - Rico Berner
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
- Department of Physics, Humboldt Universität zu Berlin, Berlin, Germany
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3
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Zheng Z, Xu C, Fan J, Liu M, Chen X. Order parameter dynamics in complex systems: From models to data. CHAOS (WOODBURY, N.Y.) 2024; 34:022101. [PMID: 38341762 DOI: 10.1063/5.0180340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 12/14/2023] [Indexed: 02/13/2024]
Abstract
Collective ordering behaviors are typical macroscopic manifestations embedded in complex systems and can be ubiquitously observed across various physical backgrounds. Elements in complex systems may self-organize via mutual or external couplings to achieve diverse spatiotemporal coordinations. The order parameter, as a powerful quantity in describing the transition to collective states, may emerge spontaneously from large numbers of degrees of freedom through competitions. In this minireview, we extensively discussed the collective dynamics of complex systems from the viewpoint of order-parameter dynamics. A synergetic theory is adopted as the foundation of order-parameter dynamics, and it focuses on the self-organization and collective behaviors of complex systems. At the onset of macroscopic transitions, slow modes are distinguished from fast modes and act as order parameters, whose evolution can be established in terms of the slaving principle. We explore order-parameter dynamics in both model-based and data-based scenarios. For situations where microscopic dynamics modeling is available, as prototype examples, synchronization of coupled phase oscillators, chimera states, and neuron network dynamics are analytically studied, and the order-parameter dynamics is constructed in terms of reduction procedures such as the Ott-Antonsen ansatz, the Lorentz ansatz, and so on. For complicated systems highly challenging to be well modeled, we proposed the eigen-microstate approach (EMP) to reconstruct the macroscopic order-parameter dynamics, where the spatiotemporal evolution brought by big data can be well decomposed into eigenmodes, and the macroscopic collective behavior can be traced by Bose-Einstein condensation-like transitions and the emergence of dominant eigenmodes. The EMP is successfully applied to some typical examples, such as phase transitions in the Ising model, climate dynamics in earth systems, fluctuation patterns in stock markets, and collective motion in living systems.
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Affiliation(s)
- Zhigang Zheng
- Institute of Systems Science, Huaqiao University, Xiamen 361021, China and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
| | - Can Xu
- Institute of Systems Science, Huaqiao University, Xiamen 361021, China and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
| | - Jingfang Fan
- School of Systems Science, Beijing Normal University, Beijing 100875, China and Institute of Nonequilibrium Systems, Beijing Normal University, Beijing 100875, China
| | - Maoxin Liu
- School of Systems Science, Beijing Normal University, Beijing 100875, China and Institute of Nonequilibrium Systems, Beijing Normal University, Beijing 100875, China
| | - Xiaosong Chen
- School of Systems Science, Beijing Normal University, Beijing 100875, China and Institute of Nonequilibrium Systems, Beijing Normal University, Beijing 100875, China
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4
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Bröhl T, Rings T, Pukropski J, von Wrede R, Lehnertz K. The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 3:1338864. [PMID: 38293249 PMCID: PMC10825060 DOI: 10.3389/fnetp.2023.1338864] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Accepted: 12/19/2023] [Indexed: 02/01/2024]
Abstract
Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.
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Affiliation(s)
- Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Jan Pukropski
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - Randi von Wrede
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
- Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
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5
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Ehstand N, Donner RV, López C, Hernández-García E. Network percolation provides early warnings of abrupt changes in coupled oscillatory systems: An explanatory analysis. Phys Rev E 2023; 108:054207. [PMID: 38115534 DOI: 10.1103/physreve.108.054207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Accepted: 10/02/2023] [Indexed: 12/21/2023]
Abstract
Functional networks are powerful tools to study statistical interdependency structures in spatially extended or multivariable systems. They have been used to get insights into the dynamics of complex systems in various areas of science. In particular, percolation properties of correlation networks have been employed to identify early warning signals of critical transitions. In this work, we further investigate the corresponding potential of percolation measures for the anticipation of different types of sudden shifts in the state of coupled irregularly oscillating systems. As a paradigmatic model system, we study the dynamics of a ring of diffusively coupled noisy FitzHugh-Nagumo oscillators and show that, when the oscillators are nearly completely synchronized, the percolation-based precursors successfully provide very early warnings of the rapid switches between the two states of the system. We clarify the mechanisms behind the percolation transition by separating global trends given by the mean-field behavior from the synchronization of individual stochastic fluctuations. We then apply the same methodology to real-world data of sea surface temperature anomalies during different phases of the El Niño-Southern Oscillation. This leads to a better understanding of the factors that make percolation precursors effective as early warning indicators of incipient El Niño and La Niña events.
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Affiliation(s)
- Noémie Ehstand
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Reik V Donner
- Department of Water, Environment, Construction and Safety, Magdeburg-Stendal University of Applied Sciences, Breitscheidstraße 2, D-39114 Magdeburg, Germany
- Research Department IV-Complexity Science and Research Department I-Earth System Analysis, Potsdam Institute for Climate Impact Research (PIK)-Member of the Leibniz Association, Telegrafenberg A31, D-14473 Potsdam, Germany
| | - Cristóbal López
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Emilio Hernández-García
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
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6
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Yamada Y, Inaba K. Detecting partial synchrony in a complex oscillatory network using pseudovortices. Phys Rev E 2023; 108:024307. [PMID: 37723738 DOI: 10.1103/physreve.108.024307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 06/23/2023] [Indexed: 09/20/2023]
Abstract
Partial synchronization is an important dynamical process of coupled oscillators on various natural and artificial networks, which can remain undetected due to the system complexity. With an analogy between pairwise asynchrony of oscillators and topological defects, i.e., vortices, in the two-dimensional XY model, we propose a robust and data-driven method to identify the partial synchronization on complex networks. The proposed method is based on an integer matrix whose element is pseudovorticity that discretely quantifies asynchronous phase dynamics in every two oscillators, which results in graphical and entropic representations of partial synchrony. As a first trial, we apply our method to 200 FitzHugh-Nagumo neurons on a complex small-world network. Partially synchronized chimera states are revealed by discriminating synchronized states even with phase lags. Such phase lags also appear in partial synchronization in chimera states. Our topological, graphical, and entropic method is implemented solely with measurable phase dynamics data, which will lead to a straightforward application to general oscillatory networks including neural networks in the brain.
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Affiliation(s)
- Yasuhiro Yamada
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Kensuke Inaba
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
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7
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Rybalko A, Fradkov A. Identification of two-neuron FitzHugh-Nagumo model based on the speed-gradient and filtering. CHAOS (WOODBURY, N.Y.) 2023; 33:083126. [PMID: 37549118 DOI: 10.1063/5.0159132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2023] [Accepted: 07/19/2023] [Indexed: 08/09/2023]
Abstract
The paper is devoted to the parameter identification problem for two-neuron FitzHugh-Nagumo models under condition when only one variable, namely, the membrane potential, is measured. Another practical assumption is that both variable derivatives cannot be measured. Finally, it is assumed that the sensor measuring the membrane potential is imprecise, and all measurements have some unknown scaling factor. These circumstances bring additional difficulties to the parameters' estimation problem, and therefore, such case was not studied before. To solve the problem first, the model is transformed to a more simple form without unmeasurable variables. Variables obtained from applying a second-order real filter-differentiator are used instead of unmeasurable derivatives. Then, an adaptive system, parameters of which are estimates of original system parameters, is designed. The estimation (identification) goal is to properly adjust parameter estimates. To this end, the speed-gradient method is employed. The correctness of the obtained solution is proved theoretically and illustrated by computer simulation in the Simulink environment. The sufficient conditions of asymptotically correct identification for the speed-gradient method with integral objective function are formulated and proved. The novelty of the paper is that in contrast to existing solutions to the FitzHugh-Nagumo identification problem, we take into account a systematic error of the membrane potential measurement. Furthermore, the parameters are estimated for a system composed of two FitzHugh-Nagumo models, which open perspectives for using the proposed results for modeling and estimation of parameters for neuron population.
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Affiliation(s)
- A Rybalko
- Institute for Problems in Mechanical Engineering, RAS, Saint Petersburg 199178, Russia
- Theoretical Cybernetics Department, SPBU, Saint Petersburg 199034, Russia
| | - A Fradkov
- Institute for Problems in Mechanical Engineering, RAS, Saint Petersburg 199178, Russia
- Theoretical Cybernetics Department, SPBU, Saint Petersburg 199034, Russia
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8
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Sakaguchi H, Yamasaki K. Suppression and frequency control of repetitive spiking in the FitzHugh-Nagumo model. Phys Rev E 2023; 108:014207. [PMID: 37583215 DOI: 10.1103/physreve.108.014207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 07/07/2023] [Indexed: 08/17/2023]
Abstract
The FitzHugh-Nagumo equation is a simple model equation that exhibits spiking. The output signal of a neuron is represented in the spiking frequency or firing rate. We consider a few control methods for spiking from the viewpoint of nonlinear dynamics. The repetitive spiking can be suppressed in the FitzHugh-Nagumo model by the periodic sinusoidal force with high frequency. We study the transition to the suppressed state numerically and perform a linear stability analysis to understand the suppression of the spiking. Next, we study coupled FitzHugh-Nagumo equations. We find that the periodic forcing makes the system chaotic, and the desynchronization induced by chaos weakens the total output of spiking in a certain parameter range. Finally, we propose a method of feedback control for the spiking frequency. We can get the desired spiking and bursting frequency using this feedback control. The feedback control method is analyzed using a mapping for the input.
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Affiliation(s)
- Hidetsugu Sakaguchi
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
| | - Keito Yamasaki
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
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9
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Schmitt O, Eipert P, Wang Y, Kanoke A, Rabiller G, Liu J. Connectome-based prediction of functional impairment in experimental stroke models. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.05.05.539601. [PMID: 37205373 PMCID: PMC10187266 DOI: 10.1101/2023.05.05.539601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Experimental rat models of stroke and hemorrhage are important tools to investigate cerebrovascular disease pathophysiology mechanisms, yet how significant patterns of functional impairment induced in various models of stroke are related to changes in connectivity at the level of neuronal populations and mesoscopic parcellations of rat brains remain unresolved. To address this gap in knowledge, we employed two middle cerebral artery occlusion models and one intracerebral hemorrhage model with variant extent and location of neuronal dysfunction. Motor and spatial memory function was assessed and the level of hippocampal activation via Fos immunohistochemistry. Contribution of connectivity change to functional impairment was analyzed for connection similarities, graph distances and spatial distances as well as the importance of regions in terms of network architecture based on the neuroVIISAS rat connectome. We found that functional impairment correlated with not only the extent but also the locations of the injury among the models. In addition, via coactivation analysis in dynamic rat brain models, we found that lesioned regions led to stronger coactivations with motor function and spatial learning regions than with other unaffected regions of the connectome. Dynamic modeling with the weighted bilateral connectome detected changes in signal propagation in the remote hippocampus in all 3 stroke types, predicting the extent of hippocampal hypoactivation and impairment in spatial learning and memory function. Our study provides a comprehensive analytical framework in predictive identification of remote regions not directly altered by stroke events and their functional implication.
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Affiliation(s)
- Oliver Schmitt
- Medical School Hamburg - University of Applied Sciences, Department of Anatomy; University of Rostock, Institute of Anatomy
- SFVAMC, 1700 Owens Street, San Francisco, CA 94158
| | - Peter Eipert
- Medical School Hamburg - University of Applied Sciences, Department of Anatomy; University of Rostock, Institute of Anatomy
- SFVAMC, 1700 Owens Street, San Francisco, CA 94158
| | - Yonggang Wang
- Department of Neurological Surgery, UCSF
- SFVAMC, 1700 Owens Street, San Francisco, CA 94158
- Department of Neurological Surgery, Beijing Tiantan Hospital, Capital Medical University, Beijing, PR China, 100050
| | - Atsushi Kanoke
- Department of Neurological Surgery, UCSF
- SFVAMC, 1700 Owens Street, San Francisco, CA 94158
- Department of Neurosurgery, Tohoku University Graduate School of Medicine, 1-1 Seiryo-machi, Aoba-ku, Sendai 980-8574, Japan
| | - Gratianne Rabiller
- Department of Neurological Surgery, UCSF
- SFVAMC, 1700 Owens Street, San Francisco, CA 94158
| | - Jialing Liu
- Department of Neurological Surgery, UCSF
- SFVAMC, 1700 Owens Street, San Francisco, CA 94158
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10
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Andrzejak RG, Espinoso A. Chimera states in multiplex networks: Chameleon-like across-layer synchronization. CHAOS (WOODBURY, N.Y.) 2023; 33:2890080. [PMID: 37163994 DOI: 10.1063/5.0146550] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Accepted: 04/19/2023] [Indexed: 05/12/2023]
Abstract
Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators' mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups' position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag.
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Affiliation(s)
- Ralph G Andrzejak
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
| | - Anaïs Espinoso
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
- Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology, Carrer Baldiri Reixac 10-12, 08028 Barcelona, Catalonia, Spain
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11
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Mbouna SGN, Banerjee T, Schöll E. Chimera patterns with spatial random swings between periodic attractors in a network of FitzHugh-Nagumo oscillators. Phys Rev E 2023; 107:054204. [PMID: 37329071 DOI: 10.1103/physreve.107.054204] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 04/21/2023] [Indexed: 06/18/2023]
Abstract
For the study of symmetry-breaking phenomena in neuronal networks, simplified versions of the FitzHugh-Nagumo model are widely used. In this paper, these phenomena are investigated in a network of FitzHugh-Nagumo oscillators taken in the form of the original model and it is found that it exhibits diverse partial synchronization patterns that are unobserved in the networks with simplified models. Apart from the classical chimera, we report a new type of chimera pattern whose incoherent clusters are characterized by spatial random swings among a few fixed periodic attractors. Another peculiar hybrid state is found that combines the features of this chimera state and a solitary state such that the main coherent cluster is interspersed with some nodes with identical solitary dynamics. In addition, oscillation death including chimera death emerges in this network. A reduced model of the network is derived to study oscillation death, which helps explaining the transition from spatial chaos to oscillation death via the chimera state with a solitary state. This study deepens our understanding of chimera patterns in neuronal networks.
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Affiliation(s)
- S G Ngueuteu Mbouna
- Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaoundé I, P. O. Box 812, Yaoundé, Cameroon
| | - Tanmoy Banerjee
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, India
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany; Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany; and Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, 10115 Berlin, Germany
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12
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Jiang L, He J, Pan H, Wu D, Jiang T, Liu J. Seizure detection algorithm based on improved functional brain network structure feature extraction. Biomed Signal Process Control 2023. [DOI: 10.1016/j.bspc.2022.104053] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
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13
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Liu W, Xie J, Liu H, Xiao J. Heterogeneity induced splay state of amplitude envelope in globally coupled oscillators. CHAOS (WOODBURY, N.Y.) 2022; 32:123117. [PMID: 36587328 DOI: 10.1063/5.0130753] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2022] [Accepted: 11/11/2022] [Indexed: 06/17/2023]
Abstract
Splay states of the amplitude envelope are stably observed as a heterogenous node is introduced into the globally coupled identical oscillators with repulsive coupling. With the increment of the frequency mismatches between the heterogenous nodes and the rest identical globally coupled oscillators, the formal stable splay state based on the time series becomes unstable, while a splay state based on the new-born amplitude envelopes of time series is stably observed among the rest identical oscillators. The characteristics of the splay state based on the amplitude envelope are numerically and theoretically presented for different parameters of the coupling strength ϵ and the frequency mismatches Δω for small coupling strength and large frequency mismatches. We expect that all these results could reveal the generality of splay states in coupled nonidentical oscillators and help to understand the rich dynamics of amplitude envelopes in multidisciplinary fields.
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Affiliation(s)
- Weiqing Liu
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Jiangnan Xie
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Hanchang Liu
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Jinghua Xiao
- School of Science, Beijing University of Posts and Communications, Beijing 100876, China
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14
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Ramasamy M, Kumarasamy S, Srinivasan A, Subburam P, Rajagopal K. Dynamical effects of hypergraph links in a network of fractional-order complex systems. CHAOS (WOODBURY, N.Y.) 2022; 32:123128. [PMID: 36587325 DOI: 10.1063/5.0103241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 11/14/2022] [Indexed: 06/17/2023]
Abstract
In recent times, the fractional-order dynamical networks have gained lots of interest across various scientific communities because it admits some important properties like infinite memory, genetic characteristics, and more degrees of freedom than an integer-order system. Because of these potential applications, the study of the collective behaviors of fractional-order complex networks has been investigated in the literature. In this work, we investigate the influence of higher-order interactions in fractional-order complex systems. We consider both two-body and three-body diffusive interactions. To elucidate the role of higher-order interaction, we show how the network of oscillators is synchronized for different values of fractional-order. The stability of synchronization is studied with a master stability function analysis. Our results show that higher-order interactions among complex networks help the earlier synchronization of networks with a lesser value of first-order coupling strengths in fractional-order complex simplices. Besides that, the fractional-order also shows a notable impact on synchronization of complex simplices. For the lower value of fractional-order, the systems get synchronized earlier, with lesser coupling strengths in both two-body and three-body interactions. To show the generality in the outcome, two neuron models, namely, Hindmarsh-Rose and Morris-Leccar, and a nonlinear Rössler oscillator are considered for our analysis.
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Affiliation(s)
- Mohanasubha Ramasamy
- Centre for Computational Modeling, Chennai Institute of Technology, Chennai 600069, India
| | - Suresh Kumarasamy
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - Ashokkumar Srinivasan
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - Pavithra Subburam
- Department of Biomedical Engineering, Chennai Institute of Technology, Chennai 600069, India
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
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15
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Arvin S, Yonehara K, Glud AN. Therapeutic Neuromodulation toward a Critical State May Serve as a General Treatment Strategy. Biomedicines 2022; 10:biomedicines10092317. [PMID: 36140418 PMCID: PMC9496064 DOI: 10.3390/biomedicines10092317] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Revised: 09/11/2022] [Accepted: 09/14/2022] [Indexed: 11/18/2022] Open
Abstract
Brain disease has become one of this century’s biggest health challenges, urging the development of novel, more effective treatments. To this end, neuromodulation represents an excellent method to modulate the activity of distinct neuronal regions to alleviate disease. Recently, the medical indications for neuromodulation therapy have expanded through the adoption of the idea that neurological disorders emerge from deficits in systems-level structures, such as brain waves and neural topology. Connections between neuronal regions are thought to fluidly form and dissolve again based on the patterns by which neuronal populations synchronize. Akin to a fire that may spread or die out, the brain’s activity may similarly hyper-synchronize and ignite, such as seizures, or dwindle out and go stale, as in a state of coma. Remarkably, however, the healthy brain remains hedged in between these extremes in a critical state around which neuronal activity maneuvers local and global operational modes. While it has been suggested that perturbations of this criticality could underlie neuropathologies, such as vegetative states, epilepsy, and schizophrenia, a major translational impact is yet to be made. In this hypothesis article, we dissect recent computational findings demonstrating that a neural network’s short- and long-range connections have distinct and tractable roles in sustaining the critical regime. While short-range connections shape the dynamics of neuronal activity, long-range connections determine the scope of the neuronal processes. Thus, to facilitate translational progress, we introduce topological and dynamical system concepts within the framework of criticality and discuss the implications and possibilities for therapeutic neuromodulation guided by topological decompositions.
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Affiliation(s)
- Simon Arvin
- Center for Experimental Neuroscience—CENSE, Department of Neurosurgery, Aarhus University Hospital, Palle Juul-Jensens Boulevard 165, 8200 Aarhus N, Denmark
- Danish Research Institute of Translational Neuroscience—DANDRITE, Nordic-EMBL Partnership for Molecular Medicine, Department of Biomedicine, Aarhus University, Ole Worms Allé 8, 8000 Aarhus C, Denmark
- Department of Neurosurgery, Department of Clinical Medicine, Aarhus University, Palle Juul-Jensens Boulevard 11 Building A, 8200 Aarhus N, Denmark
- Correspondence: ; Tel.: +45 6083-1275
| | - Keisuke Yonehara
- Danish Research Institute of Translational Neuroscience—DANDRITE, Nordic-EMBL Partnership for Molecular Medicine, Department of Biomedicine, Aarhus University, Ole Worms Allé 8, 8000 Aarhus C, Denmark
- Multiscale Sensory Structure Laboratory, National Institute of Genetics, Mishima, Shizuoka 411-8540, Japan
- Department of Genetics, The Graduate University for Advanced Studies (SOKENDAI), Mishima, Shizuoka 411-8540, Japan
| | - Andreas Nørgaard Glud
- Center for Experimental Neuroscience—CENSE, Department of Neurosurgery, Aarhus University Hospital, Palle Juul-Jensens Boulevard 165, 8200 Aarhus N, Denmark
- Department of Neurosurgery, Department of Clinical Medicine, Aarhus University, Palle Juul-Jensens Boulevard 11 Building A, 8200 Aarhus N, Denmark
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16
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Liu Y, Li H, Guo SX, Iu HHC. Generation of Multi-Lobe Chua Corsage Memristor and Its Neural Oscillation. MICROMACHINES 2022; 13:1330. [PMID: 36014252 PMCID: PMC9414626 DOI: 10.3390/mi13081330] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/12/2022] [Revised: 08/05/2022] [Accepted: 08/11/2022] [Indexed: 06/15/2023]
Abstract
The Chua corsage memristor (CCM) is considered as one of the candidates for the realization of biological neuron models due to its rich neuromorphic behaviors. In this paper, a universal model for m-lobe CCM memristor is proposed. Moreover, a novel small-signal equivalent circuit with one capacitor is derived based on the proposed model to determine the edge of chaos and obtain the zero-pole diagrams and analyze the frequency response and oscillation mechanism of the m-lobe CCM system, which are discussed in detail. In view of existence of the edge of chaos, the frequency response and the oscillation mechanism of the simplest oscillator is analysed using the proposed model. Finally, the proposed model has exhibited some essential neural oscillation, including the stable limit cycle, supercritical Hopf bifurcation, spiking and bursting oscillation. This study also reveals a previously undiscovered behavior of bursting oscillation in a CCM system.
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Affiliation(s)
- Yue Liu
- Department of Electrical and Electronic Engineering, Changchun University of Technology, Changchun 130012, China
| | - Hui Li
- Department of Electrical and Electronic Engineering, Changchun University of Technology, Changchun 130012, China
| | - Shu-Xu Guo
- College of Electronic Science and Engineering, Jilin University, Changchun 130012, China
| | - Herbert Ho-Ching Iu
- Department of Electrical, Electronic and Computer Engineering, The University of Western Australia, Crawley, WA 6009, Australia
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17
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Human brain structural connectivity matrices-ready for modelling. Sci Data 2022; 9:486. [PMID: 35945231 PMCID: PMC9363436 DOI: 10.1038/s41597-022-01596-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Accepted: 07/25/2022] [Indexed: 11/10/2022] Open
Abstract
The human brain represents a complex computational system, the function and structure of which may be measured using various neuroimaging techniques focusing on separate properties of the brain tissue and activity. We capture the organization of white matter fibers acquired by diffusion-weighted imaging using probabilistic diffusion tractography. By segmenting the results of tractography into larger anatomical units, it is possible to draw inferences about the structural relationships between these parts of the system. This pipeline results in a structural connectivity matrix, which contains an estimate of connection strength among all regions. However, raw data processing is complex, computationally intensive, and requires expert quality control, which may be discouraging for researchers with less experience in the field. We thus provide brain structural connectivity matrices in a form ready for modelling and analysis and thus usable by a wide community of scientists. The presented dataset contains brain structural connectivity matrices together with the underlying raw diffusion and structural data, as well as basic demographic data of 88 healthy subjects. Measurement(s) | Diffusion Weighted Imaging | Technology Type(s) | Magnetic Resonance Imaging | Sample Characteristic - Organism | Homo sapiens | Sample Characteristic - Location | Czech Republic |
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18
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Botha AE, Ansariara M, Emadi S, Kolahchi MR. Chimera Patterns of Synchrony in a Frustrated Array of Hebb Synapses. Front Comput Neurosci 2022; 16:888019. [PMID: 35814347 PMCID: PMC9260432 DOI: 10.3389/fncom.2022.888019] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2022] [Accepted: 05/30/2022] [Indexed: 11/13/2022] Open
Abstract
The union of the Kuramoto–Sakaguchi model and the Hebb dynamics reproduces the Lisman switch through a bistability in synchronized states. Here, we show that, within certain ranges of the frustration parameter, the chimera pattern can emerge, causing a different, time-evolving, distribution in the Hebbian synaptic strengths. We study the stability range of the chimera as a function of the frustration (phase-lag) parameter. Depending on the range of the frustration, two different types of chimeras can appear spontaneously, i.e., from randomized initial conditions. In the first type, the oscillators in the coherent region rotate, on average, slower than those in the incoherent region; while in the second type, the average rotational frequencies of the two regions are reversed, i.e., the coherent region runs, on average, faster than the incoherent region. We also show that non-stationary behavior at finite N can be controlled by adjusting the natural frequency of a single pacemaker oscillator. By slowly cycling the frequency of the pacemaker, we observe hysteresis in the system. Finally, we discuss how we can have a model for learning and memory.
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Affiliation(s)
- A. E. Botha
- Department of Physics, Science Campus, University of South Africa, Private Bag X6, Johannesburg, South Africa
| | - M. Ansariara
- Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
| | - S. Emadi
- Department of Biological Sciences, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
| | - M. R. Kolahchi
- Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
- *Correspondence: M. R. Kolahchi
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19
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Wang L, Fan H, Xiao J, Lan Y, Wang X. Criticality in reservoir computer of coupled phase oscillators. Phys Rev E 2022; 105:L052201. [PMID: 35706173 DOI: 10.1103/physreve.105.l052201] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 04/12/2022] [Indexed: 06/15/2023]
Abstract
Accumulating evidence shows that the cerebral cortex is operating near a critical state featured by power-law size distribution of neural avalanche activities, yet evidence of this critical state in artificial neural networks mimicking the cerebral cortex is still lacking. Here we design an artificial neural network of coupled phase oscillators and, by the technique of reservoir computing in machine learning, train it for predicting chaos. It is found that when the machine is properly trained, oscillators in the reservoir are synchronized into clusters whose sizes follow a power-law distribution. This feature, however, is absent when the machine is poorly trained. Additionally, it is found that despite the synchronization degree of the original network, once properly trained, the reservoir network is always developed to the same critical state, exemplifying the "attractor" nature of this state in machine learning. The generality of the results is verified in different reservoir models and by different target systems, and it is found that the scaling exponent of the distribution is independent of the reservoir details and the bifurcation parameters of the target system, but is modified when the dynamics of the target system is changed to a different type. The findings shed light on the nature of machine learning, and are helpful to the design of high-performance machines in physical systems.
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Affiliation(s)
- Liang Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Huawei Fan
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Jinghua Xiao
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Yueheng Lan
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Xingang Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
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20
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Thamizharasan S, Chandrasekar VK, Senthilvelan M, Berner R, Schöll E, Senthilkumar DV. Exotic states induced by coevolving connection weights and phases in complex networks. Phys Rev E 2022; 105:034312. [PMID: 35428128 DOI: 10.1103/physreve.105.034312] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Accepted: 03/07/2022] [Indexed: 06/14/2023]
Abstract
We consider an adaptive network, whose connection weights coevolve in congruence with the dynamical states of the local nodes that are under the influence of an external stimulus. The adaptive dynamical system mimics the adaptive synaptic connections common in neuronal networks. The adaptive network under external forcing displays exotic dynamical states such as itinerant chimeras whose population density of coherent and incoherent domains coevolves with the synaptic connection, bump states, and bump frequency cluster states, which do not exist in adaptive networks without forcing. In addition, the adaptive network also exhibits partial synchronization patterns such as phase and frequency clusters, forced entrained, and incoherent states. We introduce two measures for the strength of incoherence based on the standard deviation of the temporally averaged (mean) frequency and on the mean frequency to classify the emergent dynamical states as well as their transitions. We provide a two-parameter phase diagram showing the wealth of dynamical states. We additionally deduce the stability condition for the frequency-entrained state. We use the paradigmatic Kuramoto model of phase oscillators, which is a simple generic model that has been widely employed in unraveling a plethora of cooperative phenomena in natural and man-made systems.
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Affiliation(s)
- S Thamizharasan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli-620 024, Tamil Nadu, India
| | - V K Chandrasekar
- Centre for Nonlinear Science & Engineering, Department of Physics, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India
| | - M Senthilvelan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli-620 024, Tamil Nadu, India
| | - Rico Berner
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
- Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, 14473 Potsdam, Germany
- Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, Philippstraße 13, 10115 Berlin, Germany
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695 551, Kerala, India
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21
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Arvin S, Glud AN, Yonehara K. Short- and Long-Range Connections Differentially Modulate the Dynamics and State of Small-World Networks. Front Comput Neurosci 2022; 15:783474. [PMID: 35145389 PMCID: PMC8821822 DOI: 10.3389/fncom.2021.783474] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2021] [Accepted: 12/03/2021] [Indexed: 11/13/2022] Open
Abstract
The human brain contains billions of neurons that flexibly interconnect to support local and global computational spans. As neuronal activity propagates through the neural medium, it approaches a critical state hedged between ordered and disordered system regimes. Recent work demonstrates that this criticality coincides with the small-world topology, a network arrangement that accommodates both local (subcritical) and global (supercritical) system properties. On one hand, operating near criticality is thought to offer several neurocomputational advantages, e.g., high-dynamic range, efficient information capacity, and information transfer fidelity. On the other hand, aberrations from the critical state have been linked to diverse pathologies of the brain, such as post-traumatic epileptiform seizures and disorders of consciousness. Modulation of brain activity, through neuromodulation, presents an attractive mode of treatment to alleviate such neurological disorders, but a tractable neural framework is needed to facilitate clinical progress. Using a variation on the generative small-world model of Watts and Strogatz and Kuramoto's model of coupled oscillators, we show that the topological and dynamical properties of the small-world network are divided into two functional domains based on the range of connectivity, and that these domains play distinct roles in shaping the behavior of the critical state. We demonstrate that short-range network connections shape the dynamics of the system, e.g., its volatility and metastability, whereas long-range connections drive the system state, e.g., a seizure. Together, these findings lend support to combinatorial neuromodulation approaches that synergistically normalize the system dynamic while mobilizing the system state.
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Affiliation(s)
- Simon Arvin
- Department of Neurosurgery, Center for Experimental Neuroscience – CENSE, Institute of Clinical Medicine, Aarhus University Hospital, Aarhus C, Denmark
- Department of Biomedicine, Danish Research Institute of Translational Neuroscience – DANDRITE, Nordic-EMBL Partnership for Molecular Medicine, Aarhus University, Aarhus C, Denmark
- *Correspondence: Simon Arvin
| | - Andreas Nørgaard Glud
- Department of Neurosurgery, Center for Experimental Neuroscience – CENSE, Institute of Clinical Medicine, Aarhus University Hospital, Aarhus C, Denmark
| | - Keisuke Yonehara
- Department of Biomedicine, Danish Research Institute of Translational Neuroscience – DANDRITE, Nordic-EMBL Partnership for Molecular Medicine, Aarhus University, Aarhus C, Denmark
- Multiscale Sensory Structure Laboratory, National Institute of Genetics, Mishima, Japan
- Department of Genetics, The Graduate University for Advanced Studies (SOKENDAI), Mishima, Japan
- Keisuke Yonehara
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22
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Clusella P, Pietras B, Montbrió E. Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling. CHAOS (WOODBURY, N.Y.) 2022; 32:013105. [PMID: 35105122 DOI: 10.1063/5.0075285] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Accepted: 12/13/2021] [Indexed: 06/14/2023]
Abstract
We derive the Kuramoto model (KM) corresponding to a population of weakly coupled, nearly identical quadratic integrate-and-fire (QIF) neurons with both electrical and chemical coupling. The ratio of chemical to electrical coupling determines the phase lag of the characteristic sine coupling function of the KM and critically determines the synchronization properties of the network. We apply our results to uncover the presence of chimera states in two coupled populations of identical QIF neurons. We find that the presence of both electrical and chemical coupling is a necessary condition for chimera states to exist. Finally, we numerically demonstrate that chimera states gradually disappear as coupling strengths cease to be weak.
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Affiliation(s)
- Pau Clusella
- Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona Biomedical Research Park, 08003 Barcelona, Spain
| | - Bastian Pietras
- Institute of Mathematics, Technical University Berlin, 10623 Berlin, Germany
| | - Ernest Montbrió
- Neuronal Dynamics Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Spain
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23
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Berner R, Sawicki J, Thiele M, Löser T, Schöll E. Critical Parameters in Dynamic Network Modeling of Sepsis. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:904480. [PMID: 36926088 PMCID: PMC10012967 DOI: 10.3389/fnetp.2022.904480] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Accepted: 05/03/2022] [Indexed: 11/13/2022]
Abstract
In this work, we propose a dynamical systems perspective on the modeling of sepsis and its organ-damaging consequences. We develop a functional two-layer network model for sepsis based upon the interaction of parenchymal cells and immune cells via cytokines, and the coevolutionary dynamics of parenchymal, immune cells, and cytokines. By means of the simple paradigmatic model of phase oscillators in a two-layer system, we analyze the emergence of organ threatening interactions between the dysregulated immune system and the parenchyma. We demonstrate that the complex cellular cooperation between parenchyma and stroma (immune layer) either in the physiological or in the pathological case can be related to dynamical patterns of the network. In this way we explain sepsis by the dysregulation of the healthy homeostatic state (frequency synchronized) leading to a pathological state (desynchronized or multifrequency cluster) in the parenchyma. We provide insight into the complex stabilizing and destabilizing interplay of parenchyma and stroma by determining critical interaction parameters. The coupled dynamics of parenchymal cells (metabolism) and nonspecific immune cells (response of the innate immune system) is represented by nodes of a duplex layer. Cytokine interaction is modeled by adaptive coupling weights between nodes representing immune cells (with fast adaptation timescale) and parenchymal cells (slow adaptation timescale), and between pairs of parenchymal and immune cells in the duplex network (fixed bidirectional coupling). The proposed model allows for a functional description of organ dysfunction in sepsis and the recurrence risk in a plausible pathophysiological context.
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Affiliation(s)
- Rico Berner
- Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany.,Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
| | - Jakub Sawicki
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany.,Potsdam Institute for Climate Impact Research, Potsdam, Germany.,Fachhochschule Nordwestschweiz FHNW, Basel, Switzerland
| | - Max Thiele
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
| | | | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany.,Potsdam Institute for Climate Impact Research, Potsdam, Germany.,Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu Berlin, Berlin, Germany
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24
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Separating Neural Oscillations from Aperiodic 1/f Activity: Challenges and Recommendations. Neuroinformatics 2022; 20:991-1012. [PMID: 35389160 PMCID: PMC9588478 DOI: 10.1007/s12021-022-09581-8] [Citation(s) in RCA: 50] [Impact Index Per Article: 25.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 02/25/2022] [Indexed: 12/31/2022]
Abstract
Electrophysiological power spectra typically consist of two components: An aperiodic part usually following an 1/f power law [Formula: see text] and periodic components appearing as spectral peaks. While the investigation of the periodic parts, commonly referred to as neural oscillations, has received considerable attention, the study of the aperiodic part has only recently gained more interest. The periodic part is usually quantified by center frequencies, powers, and bandwidths, while the aperiodic part is parameterized by the y-intercept and the 1/f exponent [Formula: see text]. For investigation of either part, however, it is essential to separate the two components. In this article, we scrutinize two frequently used methods, FOOOF (Fitting Oscillations & One-Over-F) and IRASA (Irregular Resampling Auto-Spectral Analysis), that are commonly used to separate the periodic from the aperiodic component. We evaluate these methods using diverse spectra obtained with electroencephalography (EEG), magnetoencephalography (MEG), and local field potential (LFP) recordings relating to three independent research datasets. Each method and each dataset poses distinct challenges for the extraction of both spectral parts. The specific spectral features hindering the periodic and aperiodic separation are highlighted by simulations of power spectra emphasizing these features. Through comparison with the simulation parameters defined a priori, the parameterization error of each method is quantified. Based on the real and simulated power spectra, we evaluate the advantages of both methods, discuss common challenges, note which spectral features impede the separation, assess the computational costs, and propose recommendations on how to use them.
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25
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Sawicki J, Hartmann L, Bader R, Schöll E. Modelling the perception of music in brain network dynamics. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:910920. [PMID: 36926090 PMCID: PMC10013054 DOI: 10.3389/fnetp.2022.910920] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 07/11/2022] [Indexed: 11/13/2022]
Abstract
We analyze the influence of music in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report an increase of coherence between the global dynamics in our network and the input signal induced by a specific music song. We show that the level of coherence depends crucially on the frequency band. We compare our results with experimental data, which also describe global neural synchronization between different brain regions in the gamma-band range in a time-dependent manner correlated with musical large-scale form, showing increased synchronization just before transitions between different parts in a musical piece (musical high-level events). The results also suggest a separation in musical form-related brain synchronization between high brain frequencies, associated with neocortical activity, and low frequencies in the range of dance movements, associated with interactivity between cortical and subcortical regions.
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Affiliation(s)
- Jakub Sawicki
- Potsdam Institute for Climate Impact Research, Potsdam, Germany.,Institut für Musikpädagogik, Universität der Künste Berlin, Berlin, Germany.,Fachhochschule Nordwestschweiz FHNW, Basel, Switzerland.,Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
| | - Lenz Hartmann
- Institute of Systematic Musicology, University of Hamburg, Hamburg, Germany
| | - Rolf Bader
- Institute of Systematic Musicology, University of Hamburg, Hamburg, Germany
| | - Eckehard Schöll
- Potsdam Institute for Climate Impact Research, Potsdam, Germany.,Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany.,Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, Berlin, Germany
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26
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Fischer T, Rings T, Rahimi Tabar MR, Lehnertz K. Towards a Data-Driven Estimation of Resilience in Networked Dynamical Systems: Designing a Versatile Testbed. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:838142. [PMID: 36926066 PMCID: PMC10013011 DOI: 10.3389/fnetp.2022.838142] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 02/03/2022] [Indexed: 11/13/2022]
Abstract
Estimating resilience of adaptive, networked dynamical systems remains a challenge. Resilience refers to a system's capacity "to absorb exogenous and/or endogenous disturbances and to reorganize while undergoing change so as to still retain essentially the same functioning, structure, and feedbacks." The majority of approaches to estimate resilience requires exact knowledge of the underlying equations of motion; the few data-driven approaches so far either lack appropriate strategies to verify their suitability or remain subject of considerable debate. We develop a testbed that allows one to modify resilience of a multistable networked dynamical system in a controlled manner. The testbed also enables generation of multivariate time series of system observables to evaluate the suitability of data-driven estimators of resilience. We report first findings for such an estimator.
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Affiliation(s)
- Tobias Fischer
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany.,Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany.,Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - M Reza Rahimi Tabar
- Department of Physics, Sharif University of Technology, Tehran, Iran.,Institute of Physics, Carl von Ossietzky University of Oldenburg, Oldenburg, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany.,Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany.,Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
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27
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Goodfellow M, Andrzejak RG, Masoller C, Lehnertz K. What Models and Tools can Contribute to a Better Understanding of Brain Activity? FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:907995. [PMID: 36926061 PMCID: PMC10013030 DOI: 10.3389/fnetp.2022.907995] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 06/06/2022] [Indexed: 12/18/2022]
Abstract
Despite impressive scientific advances in understanding the structure and function of the human brain, big challenges remain. A deep understanding of healthy and aberrant brain activity at a wide range of temporal and spatial scales is needed. Here we discuss, from an interdisciplinary network perspective, the advancements in physical and mathematical modeling as well as in data analysis techniques that, in our opinion, have potential to further advance our understanding of brain structure and function.
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Affiliation(s)
- Marc Goodfellow
- Living Systems Institute, University of Exeter, Exeter, United Kingdom
| | - Ralph G Andrzejak
- Department of Information and Communication Technologies, University Pompeu Fabra, Barcelona, Spain
| | - Cristina Masoller
- Department of Physics, Universitat Politecnica de Catalunya, Barcelona, Spain
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany.,Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany.,Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
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28
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Chouzouris T, Roth N, Cakan C, Obermayer K. Applications of optimal nonlinear control to a whole-brain network of FitzHugh-Nagumo oscillators. Phys Rev E 2021; 104:024213. [PMID: 34525550 DOI: 10.1103/physreve.104.024213] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2021] [Accepted: 07/26/2021] [Indexed: 01/21/2023]
Abstract
We apply the framework of optimal nonlinear control to steer the dynamics of a whole-brain network of FitzHugh-Nagumo oscillators. Its nodes correspond to the cortical areas of an atlas-based segmentation of the human cerebral cortex, and the internode coupling strengths are derived from diffusion tensor imaging data of the connectome of the human brain. Nodes are coupled using an additive scheme without delays and are driven by background inputs with fixed mean and additive Gaussian noise. Optimal control inputs to nodes are determined by minimizing a cost functional that penalizes the deviations from a desired network dynamic, the control energy, and spatially nonsparse control inputs. Using the strength of the background input and the overall coupling strength as order parameters, the network's state-space decomposes into regions of low- and high-activity fixed points separated by a high-amplitude limit cycle, all of which qualitatively correspond to the states of an isolated network node. Along the borders, however, additional limit cycles, asynchronous states, and multistability can be observed. Optimal control is applied to several state-switching and network synchronization tasks, and the results are compared to controllability measures from linear control theory for the same connectome. We find that intuitions from the latter about the roles of nodes in steering the network dynamics, which are solely based on connectome features, do not generally carry over to nonlinear systems, as had been previously implied. Instead, the role of nodes under optimal nonlinear control critically depends on the specified task and the system's location in state space. Our results shed new light on the controllability of brain network states and may serve as an inspiration for the design of new paradigms for noninvasive brain stimulation.
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Affiliation(s)
- Teresa Chouzouris
- Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Marchstraße 23, 10587 Berlin, Germany
| | - Nicolas Roth
- Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Marchstraße 23, 10587 Berlin, Germany
| | - Caglar Cakan
- Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Marchstraße 23, 10587 Berlin, Germany.,Bernstein Center for Computational Neuroscience Berlin, Philippstraße 13, 10115 Berlin, Germany
| | - Klaus Obermayer
- Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Marchstraße 23, 10587 Berlin, Germany.,Bernstein Center for Computational Neuroscience Berlin, Philippstraße 13, 10115 Berlin, Germany
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Gerster M, Taher H, Škoch A, Hlinka J, Guye M, Bartolomei F, Jirsa V, Zakharova A, Olmi S. Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation. Front Syst Neurosci 2021; 15:675272. [PMID: 34539355 PMCID: PMC8440880 DOI: 10.3389/fnsys.2021.675272] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 07/07/2021] [Indexed: 11/13/2022] Open
Abstract
Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.
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Affiliation(s)
- Moritz Gerster
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
| | - Halgurd Taher
- Inria Sophia Antipolis Méditerranée Research Centre, MathNeuro Team, Valbonne, France
| | - Antonín Škoch
- National Institute of Mental Health, Klecany, Czechia
- MR Unit, Department of Diagnostic and Interventional Radiology, Institute for Clinical and Experimental Medicine, Prague, Czechia
| | - Jaroslav Hlinka
- National Institute of Mental Health, Klecany, Czechia
- Institute of Computer Science of the Czech Academy of Sciences, Prague, Czechia
| | - Maxime Guye
- Faculté de Médecine de la Timone, Centre de Résonance Magnétique et Biologique et Médicale (CRMBM, UMR CNRS-AMU 7339), Medical School of Marseille, Aix-Marseille Université, Marseille, France
- Assistance Publique -Hôpitaux de Marseille, Hôpital de la Timone, Pôle d'Imagerie, Marseille, France
| | - Fabrice Bartolomei
- Assistance Publique - Hôpitaux de Marseille, Hôpital de la Timone, Service de Neurophysiologie Clinique, Marseille, France
| | - Viktor Jirsa
- Aix Marseille Université, Inserm, Institut de Neurosciences des Systèmes, UMRS 1106, Marseille, France
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
| | - Simona Olmi
- Inria Sophia Antipolis Méditerranée Research Centre, MathNeuro Team, Valbonne, France
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Sesto Fiorentino, Italy
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30
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Pyragas K, Fedaravičius AP, Pyragienė T. Suppression of synchronous spiking in two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. Phys Rev E 2021; 104:014203. [PMID: 34412351 DOI: 10.1103/physreve.104.014203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2021] [Accepted: 06/14/2021] [Indexed: 01/28/2023]
Abstract
Collective oscillations and their suppression by external stimulation are analyzed in a large-scale neural network consisting of two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. In the limit of an infinite number of neurons, the microscopic model of this network can be reduced to an exact low-dimensional system of mean-field equations. Bifurcation analysis of these equations reveals three different dynamic modes in a free network: a stable resting state, a stable limit cycle, and bistability with a coexisting resting state and a limit cycle. We show that in the limit cycle mode, high-frequency stimulation of an inhibitory population can stabilize an unstable resting state and effectively suppress collective oscillations. We also show that in the bistable mode, the dynamics of the network can be switched from a stable limit cycle to a stable resting state by applying an inhibitory pulse to the excitatory population. The results obtained from the mean-field equations are confirmed by numerical simulation of the microscopic model.
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Affiliation(s)
- Kestutis Pyragas
- Department of Fundamental Research, Center for Physical Sciences and Technology, LT-10257 Vilnius, Lithuania
| | - Augustinas P Fedaravičius
- Department of Fundamental Research, Center for Physical Sciences and Technology, LT-10257 Vilnius, Lithuania
| | - Tatjana Pyragienė
- Department of Fundamental Research, Center for Physical Sciences and Technology, LT-10257 Vilnius, Lithuania
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31
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Kumarasamy S, Dudkowski D, Prasad A, Kapitaniak T. Ordered slow and fast dynamics of unsynchronized coupled phase oscillators. CHAOS (WOODBURY, N.Y.) 2021; 31:081102. [PMID: 34470238 DOI: 10.1063/5.0063513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Accepted: 08/06/2021] [Indexed: 06/13/2023]
Abstract
Slow and fast dynamics of unsynchronized coupled nonlinear oscillators is hard to extract. In this paper, we use the concept of perpetual points to explain the short duration ordering in the unsynchronized motions of the phase oscillators. We show that the coupled unsynchronized system has ordered slow and fast dynamics when it passes through the perpetual point. Our simulations of single, two, three, and 50 coupled Kuramoto oscillators show the generic nature of perpetual points in the identification of slow and fast oscillations. We also exhibit that short-time synchronization of complex networks can be understood with the help of perpetual motion of the network.
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Affiliation(s)
- Suresh Kumarasamy
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Dawid Dudkowski
- Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Awadhesh Prasad
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Tomasz Kapitaniak
- Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland
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32
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Tsigkri-DeSmedt ND, Sarlis NV, Provata A. Shooting solitaries due to small-world connectivity in leaky integrate-and-fire networks. CHAOS (WOODBURY, N.Y.) 2021; 31:083129. [PMID: 34470234 DOI: 10.1063/5.0055163] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Accepted: 07/30/2021] [Indexed: 06/13/2023]
Abstract
We study the synchronization properties in a network of leaky integrate-and-fire oscillators with nonlocal connectivity under probabilistic small-world rewiring. We demonstrate that the random links lead to the emergence of chimera-like states where the coherent regions are interrupted by scattered, short-lived solitaries; these are termed "shooting solitaries." Moreover, we provide evidence that random links enhance the appearance of chimera-like states for values of the parameter space that otherwise support synchronization. This last effect is counter-intuitive because by adding random links to the synchronous state, the system locally organizes into coherent and incoherent domains.
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Affiliation(s)
- N D Tsigkri-DeSmedt
- Section of Condensed Matter Physics, Physics Department, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, 157 84 Athens, Greece
| | - N V Sarlis
- Section of Condensed Matter Physics, Physics Department, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, 157 84 Athens, Greece
| | - A Provata
- Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos", Agia Paraskevi, 153 10 Athens, Greece
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Sawicki J, Koulen JM, Schöll E. Synchronization scenarios in three-layer networks with a hub. CHAOS (WOODBURY, N.Y.) 2021; 31:073131. [PMID: 34340334 DOI: 10.1063/5.0055835] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Accepted: 06/22/2021] [Indexed: 06/13/2023]
Abstract
We study various relay synchronization scenarios in a three-layer network, where the middle (relay) layer is a single node, i.e., a hub. The two remote layers consist of non-locally coupled rings of FitzHugh-Nagumo oscillators modeling neuronal dynamics. All nodes of the remote layers are connected to the hub. The role of the hub and its importance for the existence of chimera states are investigated in dependence on the inter-layer coupling strength and inter-layer time delay. Tongue-like regions in the parameter plane exhibiting double chimeras, i.e., chimera states in the remote layers whose coherent cores are synchronized with each other, and salt-and-pepper states are found. At very low intra-layer coupling strength, when chimera states do not exist in single layers, these may be induced by the hub. Also, the influence of the dilution of links between the remote layers and the hub upon the dynamics is investigated. The greatest effect of dilution is observed when links to the coherent domain of the chimeras are removed.
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Affiliation(s)
- Jakub Sawicki
- Potsdam Institute for Climate Impact Research, Telegrafenberg A, 31, 14473 Potsdam, Germany
| | - Julia M Koulen
- Potsdam Institute for Climate Impact Research, Telegrafenberg A, 31, 14473 Potsdam, Germany
| | - Eckehard Schöll
- Potsdam Institute for Climate Impact Research, Telegrafenberg A, 31, 14473 Potsdam, Germany
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34
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Berner R, Yanchuk S, Maistrenko Y, Schöll E. Generalized splay states in phase oscillator networks. CHAOS (WOODBURY, N.Y.) 2021; 31:073128. [PMID: 34340340 DOI: 10.1063/5.0056664] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Accepted: 06/24/2021] [Indexed: 06/13/2023]
Abstract
Networks of coupled phase oscillators play an important role in the analysis of emergent collective phenomena. In this article, we introduce generalized m-splay states constituting a special subclass of phase-locked states with vanishing mth order parameter. Such states typically manifest incoherent dynamics, and they often create high-dimensional families of solutions (splay manifolds). For a general class of phase oscillator networks, we provide explicit linear stability conditions for splay states and exemplify our results with the well-known Kuramoto-Sakaguchi model. Importantly, our stability conditions are expressed in terms of just a few observables such as the order parameter or the trace of the Jacobian. As a result, these conditions are simple and applicable to networks of arbitrary size. We generalize our findings to phase oscillators with inertia and adaptively coupled phase oscillator models.
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Affiliation(s)
- Rico Berner
- Institute of Theoretical Physics, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - Serhiy Yanchuk
- Institute of Mathematics, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany
| | - Yuri Maistrenko
- Forschungszentrum Jülich GmbH, Wilhelm-Johnen-Straße, 52428 Jülich, Germany
| | - Eckehard Schöll
- Institute of Theoretical Physics, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
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35
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O’Hare L, Asher JM, Hibbard PB. Migraine Visual Aura and Cortical Spreading Depression-Linking Mathematical Models to Empirical Evidence. Vision (Basel) 2021; 5:30. [PMID: 34200625 PMCID: PMC8293461 DOI: 10.3390/vision5020030] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Revised: 05/15/2021] [Accepted: 05/24/2021] [Indexed: 01/10/2023] Open
Abstract
This review describes the subjective experience of visual aura in migraine, outlines theoretical models of this phenomenon, and explores how these may be linked to neurochemical, electrophysiological, and psychophysical differences in sensory processing that have been reported in migraine with aura. Reaction-diffusion models have been used to model the hallucinations thought to arise from cortical spreading depolarisation and depression in migraine aura. One aim of this review is to make the underlying principles of these models accessible to a general readership. Cortical spreading depolarisation and depression in these models depends on the balance of the diffusion rate between excitation and inhibition and the occurrence of a large spike in activity to initiate spontaneous pattern formation. We review experimental evidence, including recordings of brain activity made during the aura and attack phase, self-reported triggers of migraine, and psychophysical studies of visual processing in migraine with aura, and how these might relate to mechanisms of excitability that make some people susceptible to aura. Increased cortical excitability, increased neural noise, and fluctuations in oscillatory activity across the migraine cycle are all factors that are likely to contribute to the occurrence of migraine aura. There remain many outstanding questions relating to the current limitations of both models and experimental evidence. Nevertheless, reaction-diffusion models, by providing an integrative theoretical framework, support the generation of testable experimental hypotheses to guide future research.
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Affiliation(s)
- Louise O’Hare
- Division of Psychology, Nottingham Trent University, Nottingham NG1 4FQ, UK
| | - Jordi M. Asher
- Department of Psychology, University of Essex, Colchester CO4 3SQ, UK; (J.M.A.); (P.B.H.)
| | - Paul B. Hibbard
- Department of Psychology, University of Essex, Colchester CO4 3SQ, UK; (J.M.A.); (P.B.H.)
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36
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Frolov N, Hramov A. Extreme synchronization events in a Kuramoto model: The interplay between resource constraints and explosive transitions. CHAOS (WOODBURY, N.Y.) 2021; 31:063103. [PMID: 34241300 DOI: 10.1063/5.0055156] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Accepted: 05/17/2021] [Indexed: 06/13/2023]
Abstract
Many living and artificial systems possess structural and dynamical properties of complex networks. One of the most exciting living networked systems is the brain, in which synchronization is an essential mechanism of its normal functioning. On the other hand, excessive synchronization in neural networks reflects undesired pathological activity, including various forms of epilepsy. In this context, network-theoretical approach and dynamical modeling may uncover deep insight into the origins of synchronization-related brain disorders. However, many models do not account for the resource consumption needed for the neural networks to synchronize. To fill this gap, we introduce a phenomenological Kuramoto model evolving under the excitability resource constraints. We demonstrate that the interplay between increased excitability and explosive synchronization induced by the hierarchical organization of the network forces the system to generate short-living extreme synchronization events, which are well-known signs of epileptic brain activity. Finally, we establish that the network units occupying the medium levels of hierarchy most strongly contribute to the birth of extreme events emphasizing the focal nature of their origin.
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Affiliation(s)
- Nikita Frolov
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, The Republic of Tatarstan, Russia
| | - Alexander Hramov
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, The Republic of Tatarstan, Russia
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Shepelev IA, Muni SS, Schöll E, Strelkova GI. Repulsive inter-layer coupling induces anti-phase synchronization. CHAOS (WOODBURY, N.Y.) 2021; 31:063116. [PMID: 34241296 DOI: 10.1063/5.0054770] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Accepted: 05/25/2021] [Indexed: 06/13/2023]
Abstract
We present numerical results for the synchronization phenomena in a bilayer network of repulsively coupled 2D lattices of van der Pol oscillators. We consider the cases when the network layers have either different or the same types of intra-layer coupling topology. When the layers are uncoupled, the lattice of van der Pol oscillators with a repulsive interaction typically demonstrates a labyrinth-like pattern, while the lattice with attractively coupled van der Pol oscillators shows a regular spiral wave structure. We reveal for the first time that repulsive inter-layer coupling leads to anti-phase synchronization of spatiotemporal structures for all considered combinations of intra-layer coupling. As a synchronization measure, we use the correlation coefficient between the symmetrical pairs of network nodes, which is always close to -1 in the case of anti-phase synchronization. We also study how the form of synchronous structures depends on the intra-layer coupling strengths when the repulsive inter-layer coupling is varied.
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Affiliation(s)
- Igor A Shepelev
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - Sishu S Muni
- School of Fundamental Sciences, Massey University, Palmerston North 4410, New Zealand
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - Galina I Strelkova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
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Bhandary S, Kaur T, Banerjee T, Dutta PS. Network resilience of FitzHugh-Nagumo neurons in the presence of nonequilibrium dynamics. Phys Rev E 2021; 103:022314. [PMID: 33736003 DOI: 10.1103/physreve.103.022314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2020] [Accepted: 02/01/2021] [Indexed: 11/07/2022]
Abstract
Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the face of perturbations. Most of the research on network resilience has focused on the transition from one equilibrium state to an alternative equilibrium state. Although the presence of nonequilibrium dynamics in some nodes may advance or delay sudden transitions in networks and give early warning signals of an impending collapse, it has not been studied much in the context of network resilience. Here we bridge this gap by studying a neuronal network model with diverse topologies, in which nonequilibrium dynamics may appear in the network even before the transition to a resting state from an active state in response to environmental stress deteriorating their external conditions. We find that the percentage of uncoupled nodes exhibiting nonequilibrium dynamics plays a vital role in determining the network's transition type. We show that a higher proportion of nodes with nonequilibrium dynamics can delay the tipping and increase networks' resilience against environmental stress, irrespective of their topology. Further, predictability of an upcoming transition weakens, as the network topology moves from regular to disordered.
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Affiliation(s)
- Subhendu Bhandary
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India
| | - Taranjot Kaur
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India
| | - Tanmoy Banerjee
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
| | - Partha Sharathi Dutta
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India
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39
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Berner R, Vock S, Schöll E, Yanchuk S. Desynchronization Transitions in Adaptive Networks. PHYSICAL REVIEW LETTERS 2021; 126:028301. [PMID: 33512200 DOI: 10.1103/physrevlett.126.028301] [Citation(s) in RCA: 29] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Revised: 11/04/2020] [Accepted: 12/15/2020] [Indexed: 06/12/2023]
Abstract
Adaptive networks change their connectivity with time, depending on their dynamical state. While synchronization in structurally static networks has been studied extensively, this problem is much more challenging for adaptive networks. In this Letter, we develop the master stability approach for a large class of adaptive networks. This approach allows for reducing the synchronization problem for adaptive networks to a low-dimensional system, by decoupling topological and dynamical properties. We show how the interplay between adaptivity and network structure gives rise to the formation of stability islands. Moreover, we report a desynchronization transition and the emergence of complex partial synchronization patterns induced by an increasing overall coupling strength. We illustrate our findings using adaptive networks of coupled phase oscillators and FitzHugh-Nagumo neurons with synaptic plasticity.
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Affiliation(s)
- Rico Berner
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
- Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
| | - Simon Vock
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, Philippstraße 13, 10115 Berlin, Germany
- Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, 14473 Potsdam, Germany
| | - Serhiy Yanchuk
- Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
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