1
|
Kromer JA, Tass PA. Coordinated reset stimulation of plastic neural networks with spatially dependent synaptic connections. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 4:1351815. [PMID: 38863734 PMCID: PMC11165135 DOI: 10.3389/fnetp.2024.1351815] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Accepted: 04/15/2024] [Indexed: 06/13/2024]
Abstract
Background Abnormal neuronal synchrony is associated with several neurological disorders, including Parkinson's disease (PD), essential tremor, dystonia, and epilepsy. Coordinated reset (CR) stimulation was developed computationally to counteract abnormal neuronal synchrony. During CR stimulation, phase-shifted stimuli are delivered to multiple stimulation sites. Computational studies in plastic neural networks reported that CR stimulation drove the networks into an attractor of a stable desynchronized state by down-regulating synaptic connections, which led to long-lasting desynchronization effects that outlasted stimulation. Later, corresponding long-lasting desynchronization and therapeutic effects were found in animal models of PD and PD patients. To date, it is unclear how spatially dependent synaptic connections, as typically observed in the brain, shape CR-induced synaptic downregulation and long-lasting effects. Methods We performed numerical simulations of networks of leaky integrate-and-fire neurons with spike-timing-dependent plasticity and spatially dependent synaptic connections to study and further improve acute and long-term responses to CR stimulation. Results The characteristic length scale of synaptic connections relative to the distance between stimulation sites plays a key role in CR parameter adjustment. In networks with short synaptic length scales, a substantial synaptic downregulation can be achieved by selecting appropriate stimulus-related parameters, such as the stimulus amplitude and shape, regardless of the employed spatiotemporal pattern of stimulus deliveries. Complex stimulus shapes can induce local connectivity patterns in the vicinity of the stimulation sites. In contrast, in networks with longer synaptic length scales, the spatiotemporal sequence of stimulus deliveries is of major importance for synaptic downregulation. In particular, rapid shuffling of the stimulus sequence is advantageous for synaptic downregulation. Conclusion Our results suggest that CR stimulation parameters can be adjusted to synaptic connectivity to further improve the long-lasting effects. Furthermore, shuffling of CR sequences is advantageous for long-lasting desynchronization effects. Our work provides important hypotheses on CR parameter selection for future preclinical and clinical studies.
Collapse
Affiliation(s)
- Justus A. Kromer
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
| | | |
Collapse
|
2
|
Yu D, Wu Y, Ding Q, Li T, Jia Y. Emergence of phase clusters and coexisting states reveals the structure-function relationship. Phys Rev E 2024; 109:054312. [PMID: 38907474 DOI: 10.1103/physreve.109.054312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2024] [Accepted: 04/30/2024] [Indexed: 06/24/2024]
Abstract
The Brain Connectome Project has made significant strides in uncovering the structural connections within the brain on various levels. This has led to the question of how brain structure and function are related. Our research explores this relationship in an adaptive neural network in which synaptic conductance between neurons follows spike-time synaptic plasticity rules. By adjusting the plasticity boundary, the network exhibits diverse collective behaviors, including phase synchronization, phase locking, hierarchical synchronization (phase clusters), and coexisting states. Using graph theory, we found that hierarchical synchronization is related to the community structure, while coexisting states are related to the hierarchical self-organizing and core-periphery structure. The network evolves into several tightly connected modules, with sparsely intermodule connections resulting in the formation of phase clusters. In addition, the hierarchical self-organizing structure facilitates the emergence of coexisting states. The coexistence state promotes the evolution of the core-periphery structure. Our results point towards the equivalence between function and structure, with function emerging from structure, and structure being influenced by function in a complex dynamic process.
Collapse
|
3
|
Thamizharasan S, Chandrasekar VK, Senthilvelan M, Senthilkumar DV. Hebbian and anti-Hebbian adaptation-induced dynamical states in adaptive networks. Phys Rev E 2024; 109:014221. [PMID: 38366486 DOI: 10.1103/physreve.109.014221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2023] [Accepted: 12/13/2023] [Indexed: 02/18/2024]
Abstract
We investigate the interplay of an external forcing and an adaptive network, whose connection weights coevolve with the dynamical states of the phase oscillators. In particular, we consider the Hebbian and anti-Hebbian adaptation mechanisms for the evolution of the connection weights. The Hebbian adaptation manifests several interesting partially synchronized states, such as phase and frequency clusters, bump state, bump frequency phase clusters, and forced entrained clusters, in addition to the completely synchronized and forced entrained states. Anti-Hebbian adaptation facilitates the manifestation of the itinerant chimera characterized by randomly evolving coherent and incoherent domains along with some of the aforementioned dynamical states induced by the Hebbian adaptation. We introduce three distinct measures for the strength of incoherence based on the local standard deviations of the time-averaged frequency and the instantaneous phase of each oscillator, and the time-averaged mean frequency for each bin to corroborate the distinct dynamical states and to demarcate the two parameter phase diagrams. We also arrive at the existence and stability conditions for the forced entrained state using the linear stability analysis, which is found to be consistent with the simulation results.
Collapse
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
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695 551, Kerala, India
| |
Collapse
|
4
|
Berner R, Lu A, Sokolov IM. Synchronization transitions in Kuramoto networks with higher-mode interaction. CHAOS (WOODBURY, N.Y.) 2023; 33:073138. [PMID: 37463093 DOI: 10.1063/5.0151038] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 06/21/2023] [Indexed: 07/20/2023]
Abstract
Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is still elusive for real-world systems in particular. We study the synchronization transition in a phase oscillator system with two nonvanishing Fourier-modes in the interaction function, hence going beyond the Kuramoto paradigm. We show that the transition scenarios crucially depend on the interplay of the two coupling modes. We describe the multistability induced by the presence of a second coupling mode. By extending the collective coordinate approach, we describe the emergence of various states observed in the transition from incoherence to coherence. Remarkably, our analysis suggests that, in essence, the two-mode coupling gives rise to states characterized by two independent but interacting groups of oscillators. We believe that these findings will stimulate future research on dynamical systems, including complex interaction functions beyond the Kuramoto-type.
Collapse
Affiliation(s)
- Rico Berner
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Annie Lu
- Department of Mathematics, Washington State University, Pullman, Washington 99164-3113, USA
| | - Igor M Sokolov
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| |
Collapse
|
5
|
Sawicki J, Berner R, Loos SAM, Anvari M, Bader R, Barfuss W, Botta N, Brede N, Franović I, Gauthier DJ, Goldt S, Hajizadeh A, Hövel P, Karin O, Lorenz-Spreen P, Miehl C, Mölter J, Olmi S, Schöll E, Seif A, Tass PA, Volpe G, Yanchuk S, Kurths J. Perspectives on adaptive dynamical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:071501. [PMID: 37486668 DOI: 10.1063/5.0147231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 05/24/2023] [Indexed: 07/25/2023]
Abstract
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.
Collapse
Affiliation(s)
- Jakub Sawicki
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Rico Berner
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Sarah A M Loos
- DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Mehrnaz Anvari
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Fraunhofer Institute for Algorithms and Scientific Computing, Schloss Birlinghoven, 53757 Sankt-Augustin, Germany
| | - Rolf Bader
- Institute of Systematic Musicology, University of Hamburg, Hamburg, Germany
| | - Wolfram Barfuss
- Transdisciplinary Research Area: Sustainable Futures, University of Bonn, 53113 Bonn, Germany
- Center for Development Research (ZEF), University of Bonn, 53113 Bonn, Germany
| | - Nicola Botta
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Computer Science and Engineering, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Nuria Brede
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Computer Science, University of Potsdam, An der Bahn 2, 14476 Potsdam, Germany
| | - Igor Franović
- Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
| | - Daniel J Gauthier
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
| | - Sebastian Goldt
- Department of Physics, International School of Advanced Studies (SISSA), Trieste, Italy
| | - Aida Hajizadeh
- Research Group Comparative Neuroscience, Leibniz Institute for Neurobiology, Magdeburg, Germany
| | - Philipp Hövel
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
| | - Omer Karin
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Philipp Lorenz-Spreen
- Center for Adaptive Rationality, Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany
| | - Christoph Miehl
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Jan Mölter
- Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, Boltzmannstraße 3, 85748 Garching bei München, Germany
| | - Simona Olmi
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Eckehard Schöll
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Alireza Seif
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Peter A Tass
- Department of Neurosurgery, Stanford University School of Medicine, Stanford, California 94304, USA
| | - Giovanni Volpe
- Department of Physics, University of Gothenburg, Gothenburg, Sweden
| | - Serhiy Yanchuk
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| |
Collapse
|
6
|
Kasatkin DV, Nekorkin VI. Transient Phase Clusters in a Two-Population Network of Kuramoto Oscillators with Heterogeneous Adaptive Interaction. ENTROPY (BASEL, SWITZERLAND) 2023; 25:913. [PMID: 37372257 DOI: 10.3390/e25060913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2023] [Revised: 05/25/2023] [Accepted: 06/07/2023] [Indexed: 06/29/2023]
Abstract
Adaptive interactions are an important property of many real-word network systems. A feature of such networks is the change in their connectivity depending on the current states of the interacting elements. In this work, we study the question of how the heterogeneous character of adaptive couplings influences the emergence of new scenarios in the collective behavior of networks. Within the framework of a two-population network of coupled phase oscillators, we analyze the role of various factors of heterogeneous interaction, such as the rules of coupling adaptation and the rate of their change in the formation of various types of coherent behavior of the network. We show that various schemes of heterogeneous adaptation lead to the formation of transient phase clusters of various types.
Collapse
Affiliation(s)
- Dmitry V Kasatkin
- A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Str., 603950 Nizhny Novgorod, Russia
| | - Vladimir I Nekorkin
- A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Str., 603950 Nizhny Novgorod, Russia
| |
Collapse
|
7
|
Jüttner B, Martens EA. Complex dynamics in adaptive phase oscillator networks. CHAOS (WOODBURY, N.Y.) 2023; 33:2888087. [PMID: 37133924 DOI: 10.1063/5.0133190] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Accepted: 03/28/2023] [Indexed: 05/04/2023]
Abstract
Networks of coupled dynamical units give rise to collective dynamics such as the synchronization of oscillators or neurons in the brain. The ability of the network to adapt coupling strengths between units in accordance with their activity arises naturally in a variety of contexts, including neural plasticity in the brain, and adds an additional layer of complexity: the dynamics on the nodes influence the dynamics of the network and vice versa. We study a minimal model of Kuramoto phase oscillators including a general adaptive learning rule with three parameters (strength of adaptivity, adaptivity offset, adaptivity shift), mimicking learning paradigms based on spike-time-dependent plasticity. Importantly, the strength of adaptivity allows to tune the system away from the limit of the classical Kuramoto model, corresponding to stationary coupling strengths and no adaptation and, thus, to systematically study the impact of adaptivity on the collective dynamics. We carry out a detailed bifurcation analysis for the minimal model consisting of N=2 oscillators. The non-adaptive Kuramoto model exhibits very simple dynamic behavior, drift, or frequency-locking; but once the strength of adaptivity exceeds a critical threshold non-trivial bifurcation structures unravel: A symmetric adaptation rule results in multi-stability and bifurcation scenarios, and an asymmetric adaptation rule generates even more intriguing and rich dynamics, including a period-doubling cascade to chaos as well as oscillations displaying features of both librations and rotations simultaneously. Generally, adaptation improves the synchronizability of the oscillators. Finally, we also numerically investigate a larger system consisting of N=50 oscillators and compare the resulting dynamics with the case of N=2 oscillators.
Collapse
Affiliation(s)
- Benjamin Jüttner
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - Erik A Martens
- Centre for Mathematical Sciences, Lund University, Sölvegatan 18B, 221 00 Lund, Sweden
- Center for Translational Neurosciences, University of Copenhagen, Blegdamsvej 3, 2200 Copenhagen, Denmark
| |
Collapse
|
8
|
Bergoin R, Torcini A, Deco G, Quoy M, Zamora-López G. Inhibitory neurons control the consolidation of neural assemblies via adaptation to selective stimuli. Sci Rep 2023; 13:6949. [PMID: 37117236 PMCID: PMC10147639 DOI: 10.1038/s41598-023-34165-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Accepted: 04/25/2023] [Indexed: 04/30/2023] Open
Abstract
Brain circuits display modular architecture at different scales of organization. Such neural assemblies are typically associated to functional specialization but the mechanisms leading to their emergence and consolidation still remain elusive. In this paper we investigate the role of inhibition in structuring new neural assemblies driven by the entrainment to various inputs. In particular, we focus on the role of partially synchronized dynamics for the creation and maintenance of structural modules in neural circuits by considering a network of excitatory and inhibitory [Formula: see text]-neurons with plastic Hebbian synapses. The learning process consists of an entrainment to temporally alternating stimuli that are applied to separate regions of the network. This entrainment leads to the emergence of modular structures. Contrary to common practice in artificial neural networks-where the acquired weights are typically frozen after the learning session-we allow for synaptic adaptation even after the learning phase. We find that the presence of inhibitory neurons in the network is crucial for the emergence and the post-learning consolidation of the modular structures. Indeed networks made of purely excitatory neurons or of neurons not respecting Dale's principle are unable to form or to maintain the modular architecture induced by the stimuli. We also demonstrate that the number of inhibitory neurons in the network is directly related to the maximal number of neural assemblies that can be consolidated, supporting the idea that inhibition has a direct impact on the memory capacity of the neural network.
Collapse
Affiliation(s)
- Raphaël Bergoin
- ETIS, UMR 8051, ENSEA, CY Cergy Paris Université, CNRS, 6 Av. du Ponceau, 95000, Cergy-Pontoise, France.
- Center for Brain and Cognition, Department of Information and Communications Technologies, Pompeu Fabra University, Carrer Ramón Trias i Fargas 25-27, 08005, Barcelona, Spain.
| | - Alessandro Torcini
- Laboratoire de Physique Théorique et Modélisation, UMR 8089, CY Cergy Paris Université, CNRS, 2 Av. Adolphe Chauvin, 95032, Cergy-Pontoise, France
| | - Gustavo Deco
- Center for Brain and Cognition, Department of Information and Communications Technologies, Pompeu Fabra University, Carrer Ramón Trias i Fargas 25-27, 08005, Barcelona, Spain
- Instituciò Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluis Companys 23, 08010, Barcelona, Spain
| | - Mathias Quoy
- ETIS, UMR 8051, ENSEA, CY Cergy Paris Université, CNRS, 6 Av. du Ponceau, 95000, Cergy-Pontoise, France
- IPAL, CNRS, 1 Fusionopolis Way #21-01 Connexis (South Tower), Singapore, 138632, Singapore
| | - Gorka Zamora-López
- Center for Brain and Cognition, Department of Information and Communications Technologies, Pompeu Fabra University, Carrer Ramón Trias i Fargas 25-27, 08005, Barcelona, Spain
| |
Collapse
|
9
|
Nag Chowdhury S, Rakshit S, Hens C, Ghosh D. Interlayer antisynchronization in degree-biased duplex networks. Phys Rev E 2023; 107:034313. [PMID: 37073037 DOI: 10.1103/physreve.107.034313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Accepted: 03/09/2023] [Indexed: 04/20/2023]
Abstract
With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most previous studies consider uniform connection weights and undirected networks with positive coupling. In the present article, we incorporate the asymmetry in a two-layer multiplex network by assigning the ratio of the adjacent nodes' degrees as the weights to the intralayer edges. Despite the presence of degree-biased weighting mechanism and attractive-repulsive coupling strengths, we are able to find the necessary conditions for intralayer synchronization and interlayer antisynchronization and test whether these two macroscopic states can withstand demultiplexing in a network. During the occurrence of these two states, we analytically calculate the oscillator's amplitude. In addition to deriving the local stability conditions for interlayer antisynchronization via the master stability function approach, we also construct a suitable Lyapunov function to determine a sufficient condition for global stability. We provide numerical evidence to show the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and such repulsive interlayer coupling coefficients cannot destroy intralayer synchronization.
Collapse
Affiliation(s)
- Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, California 95616, USA
- Technology Innovation Hub (TIH), IDEAS (Institute of Data Engineering Analytics and Science Foundation), Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Sarbendu Rakshit
- Department of Mechanical Engineering, University of California, Riverside, California 92521, USA
| | - Chittaranjan Hens
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500032, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| |
Collapse
|
10
|
Fialkowski J, Yanchuk S, Sokolov IM, Schöll E, Gottwald GA, Berner R. Heterogeneous Nucleation in Finite-Size Adaptive Dynamical Networks. PHYSICAL REVIEW LETTERS 2023; 130:067402. [PMID: 36827552 DOI: 10.1103/physrevlett.130.067402] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Revised: 10/17/2022] [Accepted: 01/10/2023] [Indexed: 06/18/2023]
Abstract
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive dynamical networks feature a connectivity structure that changes over time, coevolving with the nodes' dynamical state. In this Letter, we show the emergence of two distinct first-order nonequilibrium phase transitions in a finite-size adaptive network of heterogeneous phase oscillators. Depending on the nature of defects in the internal frequency distribution, we observe either an abrupt single-step transition to full synchronization or a more gradual multistep transition. This observation has a striking resemblance to heterogeneous nucleation. We develop a mean-field approach to study the interplay between adaptivity and nodal heterogeneity and describe the dynamics of multicluster states and their role in determining the character of the phase transition. Our work provides a theoretical framework for studying the interplay between adaptivity and nodal heterogeneity.
Collapse
Affiliation(s)
- Jan Fialkowski
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Serhiy Yanchuk
- Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, 14473 Potsdam, Germany
- Institute of Mathematics, Humboldt-Universität zu Berlin, 12489 Berlin, Germany
| | - Igor M Sokolov
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
- IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, 12489 Berlin, Germany
| | - Eckehard Schöll
- Institute for Theoretical Physics, 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 zu Berlin, 10115 Berlin, Germany
| | - Georg A Gottwald
- School of Mathematics and Statistics, University of Sydney, Camperdown New South Wales 2006, Australia
| | - Rico Berner
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| |
Collapse
|
11
|
Kromer JA, Tass PA. Synaptic reshaping of plastic neuronal networks by periodic multichannel stimulation with single-pulse and burst stimuli. PLoS Comput Biol 2022; 18:e1010568. [PMID: 36327232 PMCID: PMC9632832 DOI: 10.1371/journal.pcbi.1010568] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 09/14/2022] [Indexed: 11/06/2022] Open
Abstract
Synaptic dysfunction is associated with several brain disorders, including Alzheimer's disease, Parkinson's disease (PD) and obsessive compulsive disorder (OCD). Utilizing synaptic plasticity, brain stimulation is capable of reshaping synaptic connectivity. This may pave the way for novel therapies that specifically counteract pathological synaptic connectivity. For instance, in PD, novel multichannel coordinated reset stimulation (CRS) was designed to counteract neuronal synchrony and down-regulate pathological synaptic connectivity. CRS was shown to entail long-lasting therapeutic aftereffects in PD patients and related animal models. This is in marked contrast to conventional deep brain stimulation (DBS) therapy, where PD symptoms return shortly after stimulation ceases. In the present paper, we study synaptic reshaping by periodic multichannel stimulation (PMCS) in networks of leaky integrate-and-fire (LIF) neurons with spike-timing-dependent plasticity (STDP). During PMCS, phase-shifted periodic stimulus trains are delivered to segregated neuronal subpopulations. Harnessing STDP, PMCS leads to changes of the synaptic network structure. We found that the PMCS-induced changes of the network structure depend on both the phase lags between stimuli and the shape of individual stimuli. Single-pulse stimuli and burst stimuli with low intraburst frequency down-regulate synapses between neurons receiving stimuli simultaneously. In contrast, burst stimuli with high intraburst frequency up-regulate these synapses. We derive theoretical approximations of the stimulation-induced network structure. This enables us to formulate stimulation strategies for inducing a variety of network structures. Our results provide testable hypotheses for future pre-clinical and clinical studies and suggest that periodic multichannel stimulation may be suitable for reshaping plastic neuronal networks to counteract pathological synaptic connectivity. Furthermore, we provide novel insight on how the stimulus type may affect the long-lasting outcome of conventional DBS. This may strongly impact parameter adjustment procedures for clinical DBS, which, so far, primarily focused on acute effects of stimulation.
Collapse
Affiliation(s)
- Justus A Kromer
- Department of Neurosurgery, Stanford University, Stanford, California, United States of America
| | - Peter A Tass
- Department of Neurosurgery, Stanford University, Stanford, California, United States of America
| |
Collapse
|
12
|
Franović I, Eydam S, Yanchuk S, Berner R. Collective Activity Bursting in a Population of Excitable Units Adaptively Coupled to a Pool of Resources. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:841829. [PMID: 36926089 PMCID: PMC10013072 DOI: 10.3389/fnetp.2022.841829] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 02/16/2022] [Indexed: 06/18/2023]
Abstract
We study the collective dynamics in a population of excitable units (neurons) adaptively interacting with a pool of resources. The resource pool is influenced by the average activity of the population, whereas the feedback from the resources to the population is comprised of components acting homogeneously or inhomogeneously on individual units of the population. Moreover, the resource pool dynamics is assumed to be slow and has an oscillatory degree of freedom. We show that the feedback loop between the population and the resources can give rise to collective activity bursting in the population. To explain the mechanisms behind this emergent phenomenon, we combine the Ott-Antonsen reduction for the collective dynamics of the population and singular perturbation theory to obtain a reduced system describing the interaction between the population mean field and the resources.
Collapse
Affiliation(s)
- Igor Franović
- Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Belgrade, Serbia
| | - Sebastian Eydam
- Neural Circuits and Computations Unit, RIKEN Center for Brain Science, Wako, Japan
| | - Serhiy Yanchuk
- Institut für Mathematik, Technische Universität Berlin, Berlin, Germany
- Potsdam Institute for Climate Impact Research, Potsdam, Germany
- Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Rico Berner
- Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
| |
Collapse
|
13
|
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: 3] [Impact Index Per Article: 1.5] [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.
Collapse
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
| |
Collapse
|
14
|
Sawicki J, Berner R, Löser T, Schöll E. Modeling Tumor Disease and Sepsis by Networks of Adaptively Coupled Phase Oscillators. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 1:730385. [PMID: 36925568 PMCID: PMC10013027 DOI: 10.3389/fnetp.2021.730385] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2021] [Accepted: 11/19/2021] [Indexed: 06/18/2023]
Abstract
In this study, we provide a dynamical systems perspective to the modelling of pathological states induced by tumors or infection. A unified disease model is established using the innate immune system as the reference point. We propose a two-layer network model for carcinogenesis and sepsis based upon the interaction of parenchymal cells and immune cells via cytokines, and the co-evolutionary dynamics of parenchymal, immune cells, and cytokines. Our aim is to show that the complex cellular cooperation between parenchyma and stroma (immune layer) in the physiological and pathological case can be qualitatively and functionally described by a simple paradigmatic model of phase oscillators. By this, we explain carcinogenesis, tumor progression, and sepsis by destabilization of the healthy homeostatic state (frequency synchronized), and emergence of a pathological state (desynchronized or multifrequency cluster). The coupled dynamics of parenchymal cells (metabolism) and nonspecific immune cells (reaction of innate immune system) are represented by nodes of a duplex layer. The cytokine interaction is modeled by adaptive coupling weights between the nodes representing the immune cells (with fast adaptation time scale) and the parenchymal cells (slow adaptation time scale) and between the pairs of parenchymal and immune cells in the duplex network (fixed bidirectional coupling). Thereby, carcinogenesis, organ dysfunction in sepsis, and recurrence risk can be described in a correct functional context.
Collapse
Affiliation(s)
- Jakub Sawicki
- Potsdam Institute for Climate Impact Research, Potsdam, Germany
| | - Rico Berner
- Institut für Mathematik, Technische Universität Berlin, Berlin, Germany
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, 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
| |
Collapse
|
15
|
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.
Collapse
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
| |
Collapse
|
16
|
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.
Collapse
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
| |
Collapse
|
17
|
Kasatkin DV, Nekorkin VI. Transient circulant clusters in two-population network of Kuramoto oscillators with different rules of coupling adaptation. CHAOS (WOODBURY, N.Y.) 2021; 31:073112. [PMID: 34340335 DOI: 10.1063/5.0055578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 06/21/2021] [Indexed: 06/13/2023]
Abstract
We considered a network consisting of two populations of phase oscillators, the interaction of which is determined by different rules for the coupling adaptation. The introduction of various adaptation rules leads to the suppression of splay states and the emergence of each population complex non-stationary behavior called transient circulant clusters. In such states, each population contains a pair of anti-phase clusters whose size and composition slowly change over time as a result of successive transitions of oscillators between clusters. We show that an increase in the mismatch of the adaptation rules makes it possible to stop the process of rearrangement of clusters in one or both populations of the network. Transitions to such modes are always preceded by the appearance of solitary states in one of the populations.
Collapse
Affiliation(s)
- D V Kasatkin
- Institute of Applied Physics of RAS, 46 Ul'yanov Street, 603950 Nizhny Novgorod, Russia
| | - V I Nekorkin
- Institute of Applied Physics of RAS, 46 Ul'yanov Street, 603950 Nizhny Novgorod, Russia
| |
Collapse
|
18
|
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.
Collapse
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
| |
Collapse
|
19
|
Patzauer M, Krischer K. Self-Organized Multifrequency Clusters in an Oscillating Electrochemical System with Strong Nonlinear Coupling. PHYSICAL REVIEW LETTERS 2021; 126:194101. [PMID: 34047610 DOI: 10.1103/physrevlett.126.194101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Revised: 01/26/2021] [Accepted: 04/09/2021] [Indexed: 06/12/2023]
Abstract
We study the spatiotemporal dynamics of the oscillatory photoelectrodissolution of n-type Si in a fluoride-containing electrolyte under anodic potentials using in situ ellipsometric imaging. When lowering the illumination intensity stepwise, we successively observe uniform oscillations, modulated amplitude clusters, and the coexistence of multifrequency clusters, i.e., regions with different frequencies, with a stationary domain. We argue that the multifrequency clusters emerge due to an adaptive, nonlinear, and nonlocal coupling, similar to those found in the context of neural dynamics.
Collapse
Affiliation(s)
- Maximilian Patzauer
- Nonequilibrium Chemical Physics, Department of Physics, Technical University of Munich, 85748 Garching, Germany
| | - Katharina Krischer
- Nonequilibrium Chemical Physics, Department of Physics, Technical University of Munich, 85748 Garching, Germany
| |
Collapse
|
20
|
Lanza V, Secco J, Corinto F. Blinking Networks of Memristor Oscillatory Circuits in the Flux-Charge Domain. Front Neurosci 2021; 15:618607. [PMID: 33967676 PMCID: PMC8100312 DOI: 10.3389/fnins.2021.618607] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2020] [Accepted: 03/22/2021] [Indexed: 11/23/2022] Open
Abstract
Multistability phenomena and complex nonlinear dynamics in memristor oscillators pave the way to obtain efficient solutions to optimization problems by means of novel computational architectures based on the interconnection of single–device oscillators. It is well-known that topological properties of interconnections permit to control synchronization and spatio–temporal patterns in oscillatory networks. When the interconnections can change in time with a given probability to connect two oscillators, the whole network acts as a complex network with blinking couplings. The work of has shown that a particular class of blinking complex networks are able to completely synchronize in a faster fashion with respect to other coupling strategies. This work focuses on the specific class of blinking complex networks made of Memristor–based Oscillatory Circuits (MOCs). By exploiting the recent Flux–Charge Analysis Method, we make clear that synchronization phenomena in blinking networks of memristor oscillators having stochastic couplings, i.e., Blinking Memristor Oscillatory Networks (BMONs), correspond to global periodic oscillations on invariant manifolds and the effect of a blinking link is to shift the nonlinear dynamics through the infinite (invariant) manifolds. Numerical simulations performed on MOCs prove that synchronization phenomena can be controlled just by changing the coupling amongst them.
Collapse
Affiliation(s)
- Valentina Lanza
- LMAH, FR-CNRS-3335, Université Le Havre Normandie, Le Havre, France
| | - Jacopo Secco
- Department of Electronics, Politecnico di Torino, Turin, Italy
| | | |
Collapse
|
21
|
Berner R, Yanchuk S, Schöll E. What adaptive neuronal networks teach us about power grids. Phys Rev E 2021; 103:042315. [PMID: 34005899 DOI: 10.1103/physreve.103.042315] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 04/08/2021] [Indexed: 06/12/2023]
Abstract
Power grid networks, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types of dynamical networks has attracted increasing attention over the past decade. In this paper, we provide insight into the fundamental relation between these two types of networks. For this, we consider well-established models based on phase oscillators and show their intimate relation. In particular, we prove that phase oscillator models with inertia can be viewed as a particular class of adaptive networks. This relation holds even for more general classes of power grid models that include voltage dynamics. As an immediate consequence of this relation, we discover a plethora of multicluster states for phase oscillators with inertia. Moreover, the phenomenon of cascading line failure in power grids is translated into an adaptive neuronal network.
Collapse
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
| | - Serhiy Yanchuk
- Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 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, 10115 Berlin, Germany
- Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, 14473 Potsdam, Germany
| |
Collapse
|
22
|
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: 26] [Impact Index Per Article: 8.7] [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.
Collapse
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
| |
Collapse
|
23
|
Taylor D, Skardal PS, Sun J. Introduction to Focus Issue: Symmetry and optimization in the synchronization and collective behavior of complex systems. CHAOS (WOODBURY, N.Y.) 2020; 30:060401. [PMID: 32611075 DOI: 10.1063/5.0016491] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2020] [Accepted: 06/04/2020] [Indexed: 06/11/2023]
Abstract
Synchronization phenomena and collective behavior are commonplace in complex systems with applications ranging from biological processes such as coordinated neuron firings and cell cycles to the stability of alternating current power grids. A fundamental pursuit is the study of how various types of symmetry-e.g., as manifest in network structure or coupling dynamics-impact a system's collective behavior. Understanding the intricate relations between structural and dynamical symmetry/asymmetry also provides new paths to develop strategies that enhance or inhibit synchronization. Previous research has revealed symmetry as a key factor in identifying optimization mechanisms, but the particular ways that symmetry/asymmetry influence collective behavior can generally depend on the type of dynamics, networks, and form of synchronization (e.g., phase synchronization, group synchronization, and chimera states). Other factors, such as time delay, noise, time-varying structure, multilayer connections, basin stability, and transient dynamics, also play important roles, and many of these remain underexplored. This Focus Issue brings together a survey of theoretical and applied research articles that push forward this important line of questioning.
Collapse
Affiliation(s)
- D Taylor
- Department of Mathematics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - P S Skardal
- Department of Mathematics, Trinity College, Hartford, Connecticut 06106, USA
| | - J Sun
- Clarkson Center for Complex Systems Science, Potsdam, New York 13699, USA
| |
Collapse
|
24
|
Berner R, Sawicki J, Schöll E. Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks. PHYSICAL REVIEW LETTERS 2020; 124:088301. [PMID: 32167358 DOI: 10.1103/physrevlett.124.088301] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2019] [Revised: 12/05/2019] [Accepted: 01/16/2020] [Indexed: 06/10/2023]
Abstract
We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuroscience and social sciences, as well as biology, engineering, and other disciplines. We show by theoretical analysis and computer simulations that multiplexing in a multilayer network with symmetry can induce various stable phase cluster states in a situation where they are not stable or do not even exist in the single layer. Further, we develop a method for the analysis of Laplacian matrices of multiplex networks which allows for insight into the spectral structure of these networks enabling a reduction to the stability problem of single layers. We employ the multiplex decomposition to provide analytic results for the stability of the multilayer patterns. As local dynamics we use the paradigmatic Kuramoto phase oscillator, which is a simple generic model and has been successfully applied in the modeling of synchronization phenomena in a wide range of natural and technological systems.
Collapse
Affiliation(s)
- Rico Berner
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
- Institut für Mathematik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Jakub Sawicki
- 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
| |
Collapse
|
25
|
Frequency cluster formation and slow oscillations in neural populations with plasticity. PLoS One 2019; 14:e0225094. [PMID: 31725782 PMCID: PMC6855470 DOI: 10.1371/journal.pone.0225094] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2019] [Accepted: 10/29/2019] [Indexed: 11/20/2022] Open
Abstract
We report the phenomenon of frequency clustering in a network of Hodgkin-Huxley neurons with spike timing-dependent plasticity. The clustering leads to a splitting of a neural population into a few groups synchronized at different frequencies. In this regime, the amplitude of the mean field undergoes low-frequency modulations, which may contribute to the mechanism of the emergence of slow oscillations of neural activity observed in spectral power of local field potentials or electroencephalographic signals at high frequencies. In addition to numerical simulations of such multi-clusters, we investigate the mechanisms of the observed phenomena using the simplest case of two clusters. In particular, we propose a phenomenological model which describes the dynamics of two clusters taking into account the adaptation of coupling weights. We also determine the set of plasticity functions (update rules), which lead to multi-clustering.
Collapse
|