1
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Sinha S. Emergent order in adaptively rewired networks. CHAOS (WOODBURY, N.Y.) 2024; 34:073151. [PMID: 39047160 DOI: 10.1063/5.0211829] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2024] [Accepted: 07/05/2024] [Indexed: 07/27/2024]
Abstract
We explore adaptive link change strategies that can lead a system to network configurations that yield ordered dynamical states. We propose two adaptive strategies based on feedback from the global synchronization error. In the first strategy, the connectivity matrix changes if the instantaneous synchronization error is larger than a prescribed threshold. In the second strategy, the probability of a link changing at any instant of time is proportional to the magnitude of the instantaneous synchronization error. We demonstrate that both these strategies are capable of guiding networks to chaos suppression within a prescribed tolerance, in two prototypical systems of coupled chaotic maps. So, the adaptation works effectively as an efficient search in the vast space of connectivities for a configuration that serves to yield a targeted pattern. The mean synchronization error shows the presence of a sharply defined transition to very low values after a critical coupling strength, in all cases. For the first strategy, the total time during which a network undergoes link adaptation also exhibits a distinct transition to a small value under increasing coupling strength. Analogously, for the second strategy, the mean fraction of links that change in the network over time, after transience, drops to nearly zero, after a critical coupling strength, implying that the network reaches a static link configuration that yields the desired dynamics. These ideas can then potentially help us to devise control methods for extended interactive systems, as well as suggest natural mechanisms capable of regularizing complex networks.
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Affiliation(s)
- Sudeshna Sinha
- Indian Institute of Science Education and Research Mohali, Knowledge City, SAS Nagar, Sector 81, Manauli PO 140 306, Punjab, India
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2
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Rolim Sales M, Yanchuk S, Kurths J. Recurrent chaotic clustering and slow chaos in adaptive networks. CHAOS (WOODBURY, N.Y.) 2024; 34:063144. [PMID: 38934726 DOI: 10.1063/5.0205458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2024] [Accepted: 06/05/2024] [Indexed: 06/28/2024]
Abstract
Adaptive dynamical networks are network systems in which the structure co-evolves and interacts with the dynamical state of the nodes. We study an adaptive dynamical network in which the structure changes on a slower time scale relative to the fast dynamics of the nodes. We identify a phenomenon we refer to as recurrent adaptive chaotic clustering (RACC), in which chaos is observed on a slow time scale, while the fast time scale exhibits regular dynamics. Such slow chaos is further characterized by long (relative to the fast time scale) regimes of frequency clusters or frequency-synchronized dynamics, interrupted by fast jumps between these regimes. We also determine parameter values where the time intervals between jumps are chaotic and show that such a state is robust to changes in parameters and initial conditions.
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Affiliation(s)
- Matheus Rolim Sales
- Department of Physics, São Paulo State University, Rio Claro 13506-900, SP, Brazil
- Graduate Program in Sciences, State University of Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil
- Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, P.O. Box 6012 03, Potsdam D-14412, Germany
| | - Serhiy Yanchuk
- Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, P.O. Box 6012 03, Potsdam D-14412, Germany
- School of Mathematical Sciences, University College Cork, Western Road, Cork T12 XF62, Ireland
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, P.O. Box 6012 03, Potsdam D-14412, Germany
- Institute of Physics, Humboldt University Berlin, Berlin 10099, Germany
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3
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Yadav A, Fialkowski J, Berner R, Chandrasekar VK, Senthilkumar DV. Disparity-driven heterogeneous nucleation in finite-size adaptive networks. Phys Rev E 2024; 109:L052301. [PMID: 38907508 DOI: 10.1103/physreve.109.l052301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2024] [Accepted: 04/16/2024] [Indexed: 06/24/2024]
Abstract
Phase transitions are crucial in shaping the collective dynamics of a broad spectrum of natural systems across disciplines. Here, we report two distinct heterogeneous nucleation facilitating single step and multistep phase transitions to global synchronization in a finite-size adaptive network due to the trade off between time scale adaptation and coupling strength disparities. Specifically, small intracluster nucleations coalesce either at the population interface or within the populations resulting in the two distinct phase transitions depending on the degree of the disparities. We find that the coupling strength disparity largely controls the nature of phase transition in the phase diagram irrespective of the adaptation disparity. We provide a mesoscopic description for the cluster dynamics using the collective coordinates approach that brilliantly captures the multicluster dynamics among the populations leading to distinct phase transitions. Further, we also deduce the upper bound for the coupling strength for the existence of two intraclusters explicitly in terms of adaptation and coupling strength disparities. These insights may have implications across domains ranging from neurological disorders to segregation dynamics in social networks.
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Affiliation(s)
- Akash Yadav
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695551, Kerala, India
| | - Jan Fialkowski
- Complexity Science Hub Vienna, Josefstädter Straße 39, 1080 Vienna, Austria
- Center for Medical Data Science, Medical University Vienna, Spitalgasse 23, 1090 Vienna, Austria
| | - Rico Berner
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - V K Chandrasekar
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613401, Tamil Nadu, India
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695551, Kerala, India
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4
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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.
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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
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695 551, Kerala, India
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5
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Duchet B, Bick C, Byrne Á. Mean-Field Approximations With Adaptive Coupling for Networks With Spike-Timing-Dependent Plasticity. Neural Comput 2023; 35:1481-1528. [PMID: 37437202 PMCID: PMC10422128 DOI: 10.1162/neco_a_01601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2022] [Accepted: 04/26/2023] [Indexed: 07/14/2023]
Abstract
Understanding the effect of spike-timing-dependent plasticity (STDP) is key to elucidating how neural networks change over long timescales and to design interventions aimed at modulating such networks in neurological disorders. However, progress is restricted by the significant computational cost associated with simulating neural network models with STDP and by the lack of low-dimensional description that could provide analytical insights. Phase-difference-dependent plasticity (PDDP) rules approximate STDP in phase oscillator networks, which prescribe synaptic changes based on phase differences of neuron pairs rather than differences in spike timing. Here we construct mean-field approximations for phase oscillator networks with STDP to describe part of the phase space for this very high-dimensional system. We first show that single-harmonic PDDP rules can approximate a simple form of symmetric STDP, while multiharmonic rules are required to accurately approximate causal STDP. We then derive exact expressions for the evolution of the average PDDP coupling weight in terms of network synchrony. For adaptive networks of Kuramoto oscillators that form clusters, we formulate a family of low-dimensional descriptions based on the mean-field dynamics of each cluster and average coupling weights between and within clusters. Finally, we show that such a two-cluster mean-field model can be fitted to synthetic data to provide a low-dimensional approximation of a full adaptive network with symmetric STDP. Our framework represents a step toward a low-dimensional description of adaptive networks with STDP, and could for example inform the development of new therapies aimed at maximizing the long-lasting effects of brain stimulation.
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Affiliation(s)
- Benoit Duchet
- Nuffield Department of Clinical Neuroscience, University of Oxford, Oxford X3 9DU, U.K
- MRC Brain Network Dynamics Unit, University of Oxford, Oxford X1 3TH, U.K.
| | - Christian Bick
- Department of Mathematics, Vrije Universiteit Amsterdam, Amsterdam 1081 HV, the Netherlands
- Amsterdam Neuroscience-Systems and Network Neuroscience, Amsterdam 1081 HV, the Netherlands
- Mathematical Institute, University of Oxford, Oxford X2 6GG, U.K.
| | - Áine Byrne
- School of Mathematics and Statistics, University College Dublin, Dublin D04 V1W8, Ireland
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6
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Bomela W, Singhal B, Li JS. Engineering spatiotemporal patterns: information encoding, processing, and controllability in oscillator ensembles. Biomed Phys Eng Express 2023; 9:045033. [PMID: 37348467 PMCID: PMC10486008 DOI: 10.1088/2057-1976/ace0c9] [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: 12/08/2022] [Revised: 04/21/2023] [Accepted: 06/22/2023] [Indexed: 06/24/2023]
Abstract
The ability to finely manipulate spatiotemporal patterns displayed in neuronal populations is critical for understanding and influencing brain functions, sleep cycles, and neurological pathologies. However, such control tasks are challenged not only by the immense scale but also by the lack of real-time state measurements of neurons in the population, which deteriorates the control performance. In this paper, we formulate the control of dynamic structures in an ensemble of neuron oscillators as a tracking problem and propose a principled control technique for designing optimal stimuli that produce desired spatiotemporal patterns in a network of interacting neurons without requiring feedback information. We further reveal an interesting presentation of information encoding and processing in a neuron ensemble in terms of its controllability property. The performance of the presented technique in creating complex spatiotemporal spiking patterns is demonstrated on neural populations described by mathematically ideal and biophysical models, including the Kuramoto and Hodgkin-Huxley models, as well as real-time experiments on Wein bridge oscillators.
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Affiliation(s)
- Walter Bomela
- Department of Electrical and Systems Engineering, Washington University in St. Louis,
United States of America
| | - Bharat Singhal
- Department of Electrical and Systems Engineering, Washington University in St. Louis,
United States of America
| | - Jr-Shin Li
- Department of Electrical and Systems Engineering, Washington University in St. Louis,
United States of America
- Division of Biology & and Biomedical Sciences, Washington University in St. Louis,
United States of America
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7
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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.
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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
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8
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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.
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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
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9
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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.
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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
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10
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Thiele M, Berner R, Tass PA, Schöll E, Yanchuk S. Asymmetric adaptivity induces recurrent synchronization in complex networks. CHAOS (WOODBURY, N.Y.) 2023; 33:023123. [PMID: 36859232 DOI: 10.1063/5.0128102] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 01/18/2023] [Indexed: 06/18/2023]
Abstract
Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order to fill this gap, we present a framework for describing the emergence of recurrent synchronization in complex networks with adaptive interactions. This phenomenon is manifested at the macroscopic level by temporal episodes of coherent and incoherent dynamics that alternate recurrently. At the same time, the dynamics of the individual nodes do not change qualitatively. We identify asymmetric adaptation rules and temporal separation between the adaptation and the dynamics of individual nodes as key features for the emergence of recurrent synchronization. Our results suggest that asymmetric adaptation might be a fundamental ingredient for recurrent synchronization phenomena as seen in pattern generators, e.g., in neuronal systems.
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Affiliation(s)
- Max Thiele
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
| | - Rico Berner
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
| | - Peter A Tass
- Department of Neurosurgery, Stanford University, Stanford, California 94305, USA
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
| | - Serhiy Yanchuk
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
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11
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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.
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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
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12
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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: 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.
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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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13
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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.
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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
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14
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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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15
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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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16
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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.
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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
| | - 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
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Khaledi-Nasab A, Kromer JA, Tass PA. Long-Lasting Desynchronization of Plastic Neural Networks by Random Reset Stimulation. Front Physiol 2021; 11:622620. [PMID: 33613303 PMCID: PMC7893102 DOI: 10.3389/fphys.2020.622620] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 12/23/2020] [Indexed: 12/19/2022] Open
Abstract
Excessive neuronal synchrony is a hallmark of neurological disorders such as epilepsy and Parkinson's disease. An established treatment for medically refractory Parkinson's disease is high-frequency (HF) deep brain stimulation (DBS). However, symptoms return shortly after cessation of HF-DBS. Recently developed decoupling stimulation approaches, such as Random Reset (RR) stimulation, specifically target pathological connections to achieve long-lasting desynchronization. During RR stimulation, a temporally and spatially randomized stimulus pattern is administered. However, spatial randomization, as presented so far, may be difficult to realize in a DBS-like setup due to insufficient spatial resolution. Motivated by recently developed segmented DBS electrodes with multiple stimulation sites, we present a RR stimulation protocol that copes with the limited spatial resolution of currently available depth electrodes for DBS. Specifically, spatial randomization is realized by delivering stimuli simultaneously to L randomly selected stimulation sites out of a total of M stimulation sites, which will be called L/M-RR stimulation. We study decoupling by L/M-RR stimulation in networks of excitatory integrate-and-fire neurons with spike-timing dependent plasticity by means of theoretical and computational analysis. We find that L/M-RR stimulation yields parameter-robust decoupling and long-lasting desynchronization. Furthermore, our theory reveals that strong high-frequency stimulation is not suitable for inducing long-lasting desynchronization effects. As a consequence, low and high frequency L/M-RR stimulation affect synaptic weights in qualitatively different ways. Our simulations confirm these predictions and show that qualitative differences between low and high frequency L/M-RR stimulation are present across a wide range of stimulation parameters, rendering stimulation with intermediate frequencies most efficient. Remarkably, we find that L/M-RR stimulation does not rely on a high spatial resolution, characterized by the density of stimulation sites in a target area, corresponding to a large M. In fact, L/M-RR stimulation with low resolution performs even better at low stimulation amplitudes. Our results provide computational evidence that L/M-RR stimulation may present a way to exploit modern segmented lead electrodes for long-lasting therapeutic effects.
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Affiliation(s)
- Ali Khaledi-Nasab
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
| | - Justus A Kromer
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
| | - Peter A Tass
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
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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: 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.
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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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