1
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Müller-Bender D, Radons G. Laminar chaos in systems with quasiperiodic delay. Phys Rev E 2023; 107:014205. [PMID: 36797923 DOI: 10.1103/physreve.107.014205] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Accepted: 12/15/2022] [Indexed: 06/18/2023]
Abstract
A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodic time-varying delay [Phys. Rev. Lett. 120, 084102 (2018)]0031-900710.1103/PhysRevLett.120.084102. It is characterized by nearly constant laminar phases, which are periodically interrupted by irregular bursts, where the intensity levels of the laminar phases vary chaotically from phase to phase. In this paper, we demonstrate that laminar chaos can also be observed in systems with quasiperiodic delay, where we generalize the concept of conservative and dissipative delays to such systems. It turns out that the durations of the laminar phases vary quasiperiodically and follow the dynamics of a torus map in contrast to the periodic variation observed for periodic delay. Theoretical and numerical results indicate that introducing a quasiperiodic delay modulation into a time-delay system can lead to a giant reduction of the dimension of the chaotic attractors. By varying the mean delay and keeping other parameters fixed, we found that the Kaplan-Yorke dimension is modulated quasiperiodically over several orders of magnitudes, where the dynamics switches quasiperiodically between different types of high- and low-dimensional types of chaos.
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Affiliation(s)
- David Müller-Bender
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Günter Radons
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
- ICM - Institute for Mechanical and Industrial Engineering, 09117 Chemnitz, Germany
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2
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Carlos FLP, Ubirakitan MM, Rodrigues MCA, Aguilar-Domingo M, Herrera-Gutiérrez E, Gómez-Amor J, Copelli M, Carelli PV, Matias FS. Anticipated synchronization in human EEG data: Unidirectional causality with negative phase lag. Phys Rev E 2021; 102:032216. [PMID: 33075996 DOI: 10.1103/physreve.102.032216] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2020] [Accepted: 07/15/2020] [Indexed: 11/07/2022]
Abstract
Understanding the functional connectivity of the brain has become a major goal of neuroscience. In many situations the relative phase difference, together with coherence patterns, has been employed to infer the direction of the information flow. However, it has been recently shown in local field potential data from monkeys the existence of a synchronized regime in which unidirectionally coupled areas can present both positive and negative phase differences. During the counterintuitive regime, called anticipated synchronization (AS), the phase difference does not reflect the causality. Here we investigate coherence and causality at the alpha frequency band (f∼10 Hz) between pairs of electroencephalogram (EEG) electrodes in humans during a GO/NO-GO task. We show that human EEG signals can exhibit anticipated synchronization, which is characterized by a unidirectional influence from an electrode A to an electrode B, but the electrode B leads the electrode A in time. To the best of our knowledge, this is the first verification of AS in EEG signals and in the human brain. The usual delayed synchronization (DS) regime is also present between many pairs. DS is characterized by a unidirectional influence from an electrode A to an electrode B and a positive phase difference between A and B which indicates that the electrode A leads the electrode B in time. Moreover we show that EEG signals exhibit diversity in the phase relations: the pairs of electrodes can present in-phase, antiphase, or out-of-phase synchronization with a similar distribution of positive and negative phase differences.
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Affiliation(s)
| | - Maciel-Monteiro Ubirakitan
- Grupo de Neurodinâmica, Departamento de Fisiologia e Farmacologia, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil.,Spanish Foundation for Neurometrics Development, Department of Psychophysics & Psychophysiology, 30100, Murcia, Spain
| | - Marcelo Cairrão Araújo Rodrigues
- Grupo de Neurodinâmica, Departamento de Fisiologia e Farmacologia, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| | - Moisés Aguilar-Domingo
- Spanish Foundation for Neurometrics Development, Department of Psychophysics & Psychophysiology, 30100, Murcia, Spain.,Department of Human Anatomy and Psychobiology, Faculty of Psychology, University of Murcia, 30100 Espinardo Campus, Murcia, Spain
| | - Eva Herrera-Gutiérrez
- Department of Developmental and Educational Psychology, Faculty of Psychology, University of Murcia, 30100 Espinardo Campus, Murcia, Spain
| | - Jesús Gómez-Amor
- Department of Human Anatomy and Psychobiology, Faculty of Psychology, University of Murcia, 30100 Espinardo Campus, Murcia, Spain
| | - Mauro Copelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| | - Pedro V Carelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| | - Fernanda S Matias
- Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-970 Brazil
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3
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Grover FM, Riehm C, Silva PL, Lorenz T, Riley MA. Grip force anticipation of nonlinear, underactuated load force. J Neurophysiol 2021; 125:1647-1662. [PMID: 33788625 DOI: 10.1152/jn.00616.2020] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Feedforward internal model-based control enabled by efference copies of motor commands is the prevailing theoretical account of motor anticipation. Grip force control during object manipulation-a paradigmatic example of motor anticipation-is a key line of evidence for that account. However, the internal model approach has not addressed the computational challenges faced by the act of manipulating mechanically complex objects with nonlinear, underactuated degrees of freedom. These objects exhibit complex and unpredictable load force dynamics which cannot be encoded by efference copies of underlying motor commands, leading to the prediction from the perspective of an efference copy-enabled feedforward control scheme that grip force should either lag or fail to coordinate with changes in load force. In contrast to that prediction, we found evidence for strong, precise, anticipatory grip force control during manipulations of a complex object. The results are therefore inconsistent with the internal forward model approach and suggest that efference copies of motor commands are not necessary to enable anticipatory control during active object manipulation.NEW & NOTEWORTHY From the perspective of feedforward internal model-based control, precise, anticipatory grip force (GF) control when manipulating a complex object should not be possible as the object's changing load forces (LFs) cannot be encoded by efference copies of the underlying movements. However, we observed that GF exhibited strong, precise, anticipatory coupling with LF during extended manipulations of a complex object. These findings suggest that an alternative theoretical framework is needed to account for anticipatory GF control.
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Affiliation(s)
- Francis M Grover
- Center for Cognition, Action, and Perception, Department of Psychology, University of Cincinnati, Cincinnati, Ohio.,Shirley Ryan AbilityLab, Northwestern University, Chicago, Illinois.,Edward Hines, Jr. VA Hospital, Chicago, Illinois
| | - Christopher Riehm
- Center for Cognition, Action, and Perception, Department of Psychology, University of Cincinnati, Cincinnati, Ohio
| | - Paula L Silva
- Center for Cognition, Action, and Perception, Department of Psychology, University of Cincinnati, Cincinnati, Ohio
| | - Tamara Lorenz
- Center for Cognition, Action, and Perception, Department of Psychology, University of Cincinnati, Cincinnati, Ohio.,Department of Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, Ohio.,Department of Electrical Engineering and Computer Science, University of Cincinnati, Cincinnati, Ohio
| | - Michael A Riley
- Center for Cognition, Action, and Perception, Department of Psychology, University of Cincinnati, Cincinnati, Ohio
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4
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Variable and intermittent grip force control in response to differing load force dynamics. Exp Brain Res 2018; 237:687-703. [DOI: 10.1007/s00221-018-5451-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2018] [Accepted: 12/06/2018] [Indexed: 11/26/2022]
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5
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West TO, Berthouze L, Halliday DM, Litvak V, Sharott A, Magill PJ, Farmer SF. Propagation of beta/gamma rhythms in the cortico-basal ganglia circuits of the parkinsonian rat. J Neurophysiol 2018; 119:1608-1628. [PMID: 29357448 PMCID: PMC6008089 DOI: 10.1152/jn.00629.2017] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Much of the motor impairment associated with Parkinson’s disease is thought to arise from pathological activity in the networks formed by the basal ganglia (BG) and motor cortex. To evaluate several hypotheses proposed to explain the emergence of pathological oscillations in parkinsonism, we investigated changes to the directed connectivity in BG networks following dopamine depletion. We recorded local field potentials (LFPs) in the cortex and basal ganglia of rats rendered parkinsonian by injection of 6-hydroxydopamine (6-OHDA) and in dopamine-intact controls. We performed systematic analyses of the networks using a novel tool for estimation of directed interactions (nonparametric directionality, NPD). We used a “conditioned” version of the NPD analysis that reveals the dependence of the correlation between two signals on a third reference signal. We find evidence of the dopamine dependency of both low-beta (14–20 Hz) and high-beta/low-gamma (20–40 Hz) directed network interactions. Notably, 6-OHDA lesions were associated with enhancement of the cortical “hyperdirect” connection to the subthalamic nucleus (STN) and its feedback to the cortex and striatum. We find that pathological beta synchronization resulting from 6-OHDA lesioning is widely distributed across the network and cannot be located to any individual structure. Furthermore, we provide evidence that high-beta/gamma oscillations propagate through the striatum in a pathway that is independent of STN. Rhythms at high beta/gamma show susceptibility to conditioning that indicates a hierarchical organization compared with those at low beta. These results further inform our understanding of the substrates for pathological rhythms in salient brain networks in parkinsonism. NEW & NOTEWORTHY We present a novel analysis of electrophysiological recordings in the cortico-basal ganglia network with the aim of evaluating several hypotheses concerning the origins of abnormal brain rhythms associated with Parkinson’s disease. We present evidence for changes in the directed connections within the network following chronic dopamine depletion in rodents. These findings speak to the plausibility of a “short-circuiting” of the network that gives rise to the conditions from which pathological synchronization may arise.
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Affiliation(s)
- Timothy O West
- Centre for Mathematics and Physics in the Life Sciences and Experimental Biology (CoMPLEX), Department of Physics and Astronomy, University College London , London , United Kingdom.,Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London , London , United Kingdom
| | - Luc Berthouze
- Centre for Computational Neuroscience and Robotics, University of Sussex , Falmer , United Kingdom.,UCL Great Ormond Street Institute of Child Health , London , United Kingdom
| | - David M Halliday
- Department of Electronic Engineering, University of York , York , United Kingdom
| | - Vladimir Litvak
- Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London , London , United Kingdom
| | - Andrew Sharott
- Medical Research Council Brain Network Dynamics Unit, University of Oxford , Oxford , United Kingdom
| | - Peter J Magill
- Medical Research Council Brain Network Dynamics Unit, University of Oxford , Oxford , United Kingdom.,Oxford Parkinson's Disease Centre, University of Oxford , Oxford , United Kingdom
| | - Simon F Farmer
- Department of Neurology, National Hospital for Neurology & Neurosurgery , London , United Kingdom.,Sobell Department of Motor Neuroscience and Movement Disorders, Institute of Neurology, University College London , London , United Kingdom
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6
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Müller D, Otto A, Radons G. From dynamical systems with time-varying delay to circle maps and Koopman operators. Phys Rev E 2017; 95:062214. [PMID: 28709184 DOI: 10.1103/physreve.95.062214] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2017] [Indexed: 11/07/2022]
Abstract
In this paper, we investigate the influence of the retarded access by a time-varying delay on the dynamics of delay systems. We show that there are two universality classes of delays, which lead to fundamental differences in dynamical quantities such as the Lyapunov spectrum. Therefore, we introduce an operator theoretic framework, where the solution operator of the delay system is decomposed into the Koopman operator describing the delay access and an operator similar to the solution operator known from systems with constant delay. The Koopman operator corresponds to an iterated map, called access map, which is defined by the iteration of the delayed argument of the delay equation. The dynamics of this one-dimensional iterated map determines the universality classes of the infinite-dimensional state dynamics governed by the delay differential equation. In this way, we connect the theory of time-delay systems with the theory of circle maps and the framework of the Koopman operator. In this paper, we extend our previous work [A. Otto, D. Müller, and G. Radons, Phys. Rev. Lett. 118, 044104 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.044104] by elaborating the mathematical details and presenting further results also on the Lyapunov vectors.
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Affiliation(s)
- David Müller
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Andreas Otto
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Günter Radons
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
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7
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Otto A, Müller D, Radons G. Universal Dichotomy for Dynamical Systems with Variable Delay. PHYSICAL REVIEW LETTERS 2017; 118:044104. [PMID: 28186824 DOI: 10.1103/physrevlett.118.044104] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2015] [Indexed: 06/06/2023]
Abstract
We show that the dynamics of systems with a time-dependent delay is fundamentally affected by the functional form of the retarded argument. Associating with the latter an iterated map, the access map, and a corresponding Koopman operator, we identify two universality classes. Members in the first are equivalent to systems with a constant delay. The new, second class is characterized by the mode-locking behavior of their access maps and by an asymptotically linear, instead of a logarithmic, scaling of the Lyapunov spectrum. The membership depends in a fractal manner only on the parameters of the delay.
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Affiliation(s)
- Andreas Otto
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - David Müller
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Günter Radons
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
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8
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Matias FS, Gollo LL, Carelli PV, Mirasso CR, Copelli M. Inhibitory loop robustly induces anticipated synchronization in neuronal microcircuits. Phys Rev E 2016; 94:042411. [PMID: 27841618 DOI: 10.1103/physreve.94.042411] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2016] [Indexed: 06/06/2023]
Abstract
We investigate the synchronization properties between two excitatory coupled neurons in the presence of an inhibitory loop mediated by an interneuron. Dynamic inhibition together with noise independently applied to each neuron provide phase diversity in the dynamics of the neuronal motif. We show that the interplay between the coupling strengths and the external noise controls the phase relations between the neurons in a counterintuitive way. For a master-slave configuration (unidirectional coupling) we find that the slave can anticipate the master, on average, if the slave is subject to the inhibitory feedback. In this nonusual regime, called anticipated synchronization (AS), the phase of the postsynaptic neuron is advanced with respect to that of the presynaptic neuron. We also show that the AS regime survives even in the presence of unbalanced bidirectional excitatory coupling. Moreover, for the symmetric mutually coupled situation, the neuron that is subject to the inhibitory loop leads in phase.
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Affiliation(s)
- Fernanda S Matias
- Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-970, Brazil
| | - Leonardo L Gollo
- System Neuroscience Group, Queensland Institute of Medical Research, Brisbane QLD 4006, Australia
| | - Pedro V Carelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil
| | - Claudio R Mirasso
- Instituto de Fisica Interdisciplinar y Sistemas Complejos, CSIC-UIB, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Mauro Copelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil
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9
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Abstract
Real-time prediction of signals is a task often encountered in control problems as well as by living systems. Here, a parsimonious prediction approach based on the coupling of a linear relaxation-delay system to a smooth, stationary signal is described. The resulting anticipatory relaxation dynamics (ARD) is a frequency-dependent predictor of future signal values. ARD not only approximately predicts signals on average but can anticipate the occurrence of signal peaks, too. This can be explained by recognizing ARD as an input-output system with negative group delay. It is characterized, including its prediction horizon, by its analytically given frequency response function.
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Affiliation(s)
- Henning U Voss
- Citigroup Biomedical Imaging Center, Weill Cornell Medical College, 516 East 72nd Street, New York, New York 10021, USA
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10
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Ghomsi PG, Kakmeni FMM, Tchawoua C, Kofane TC. Synchronization of cells with activator-inhibitor pathways through adaptive environment-mediated coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052911. [PMID: 26651766 DOI: 10.1103/physreve.92.052911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2015] [Indexed: 06/05/2023]
Abstract
In this paper, we report the synchronized dynamics of cells with activator-inhibitor pathways via an adaptive environment-mediated coupling scheme with feedbacks and control mechanisms. The adaptive character of the extracellular medium is modeled via its damping parameter as a physiological response aiming at annihilating the cellular differentiation existing between the chaotic biochemical pathways of the cells, in order to preserve homeostasis. We perform an investigation on the existence and stability of the synchronization manifold of the coupled system under the proposed coupling pattern. Both mathematical and computational tools suggest the accessibility of conducive prerequisites (conditions) for the emergence of a robust synchronous regime. The relevance of a phase-synchronized dynamics is appraised and several numerical indicators advocate for the prevalence of this fascinating phenomenon among the interacting cells in the phase space.
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Affiliation(s)
- P Guemkam Ghomsi
- Complex systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63 Buea-CAMEROON and Laboratoire de Mécanique, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé-Cameroon
| | - F M Moukam Kakmeni
- Complex systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63 Buea-CAMEROON and International Centre of Insect Physiology and Ecology, P.O. Box 30772-00100, Nairobi, Kenya
| | - C Tchawoua
- Laboratoire de Mécanique, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé-Cameroon
| | - T C Kofane
- Laboratoire de Mécanique, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé-Cameroon
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11
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Acharyya S, Amritkar RE. Synchronization of nearly identical dynamical systems: Size instability. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052902. [PMID: 26651757 DOI: 10.1103/physreve.92.052902] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2015] [Indexed: 06/05/2023]
Abstract
We study the generalized synchronization and its stability using the master stability function (MSF) in a network of coupled nearly identical dynamical systems. We extend the MSF approach for the case of degenerate eigenvalues of the coupling matrix. Using the MSF we study the size instability in star and ring networks for coupled nearly identical dynamical systems. In the star network of coupled Rössler systems we show that the critical size beyond which synchronization is unstable can be increased by having a larger frequency for the central node of the star. For the ring network we show that the critical size is not significantly affected by parameter variations. The results are verified by explicit numerical calculations.
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Affiliation(s)
- Suman Acharyya
- Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India
| | - R E Amritkar
- Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India
- Institute of Infrastructure, Technology, Research and Management, Khokhra Circle, Maninagar, Ahmedabad 380026, India
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12
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Self-Organized Near-Zero-Lag Synchronization Induced by Spike-Timing Dependent Plasticity in Cortical Populations. PLoS One 2015; 10:e0140504. [PMID: 26474165 PMCID: PMC4608682 DOI: 10.1371/journal.pone.0140504] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2015] [Accepted: 09/21/2015] [Indexed: 12/30/2022] Open
Abstract
Several cognitive tasks related to learning and memory exhibit synchronization of macroscopic cortical areas together with synaptic plasticity at neuronal level. Therefore, there is a growing effort among computational neuroscientists to understand the underlying mechanisms relating synchrony and plasticity in the brain. Here we numerically study the interplay between spike-timing dependent plasticity (STDP) and anticipated synchronization (AS). AS emerges when a dominant flux of information from one area to another is accompanied by a negative time lag (or phase). This means that the receiver region pulses before the sender does. In this paper we study the interplay between different synchronization regimes and STDP at the level of three-neuron microcircuits as well as cortical populations. We show that STDP can promote auto-organized zero-lag synchronization in unidirectionally coupled neuronal populations. We also find synchronization regimes with negative phase difference (AS) that are stable against plasticity. Finally, we show that the interplay between negative phase difference and STDP provides limited synaptic weight distribution without the need of imposing artificial boundaries.
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13
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Che Y, Li R, Han C, Cui S, Wang J, Wei X, Deng B. Topology identification of uncertain nonlinearly coupled complex networks with delays based on anticipatory synchronization. CHAOS (WOODBURY, N.Y.) 2013; 23:013127. [PMID: 23556964 DOI: 10.1063/1.4793541] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
This paper presents an adaptive anticipatory synchronization based method for simultaneous identification of topology and parameters of uncertain nonlinearly coupled complex dynamical networks with time delays. An adaptive controller is proposed, based on Lyapunov stability theorem and Barbǎlat's Lemma, to guarantee the stability of the anticipatory synchronization manifold between drive and response networks. Meanwhile, not only the identification criteria of network topology and system parameters are obtained but also the anticipatory time is identified. Numerical simulation results illustrate the effectiveness of the proposed method.
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Affiliation(s)
- Yanqiu Che
- Tianjin Key Laboratory of Information Sensing & Intelligent Control, Tianjin University of Technology and Education, Tianjin 300222, People's Republic of China.
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14
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Vincent UE, Nana-Nbendjo BR, McClintock PVE. Collective dynamics of a network of ratchets coupled via a stochastic dynamical environment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022913. [PMID: 23496597 DOI: 10.1103/physreve.87.022913] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2012] [Indexed: 06/01/2023]
Abstract
We investigate the collective dynamics of a network of inertia particles diffusing in a ratchet potential and interacting indirectly through their stochastic dynamical environment. We obtain analytically the condition for the existence of a stable collective state, and we show that the number N of particles in the network, and the strength k of their interaction with the environment, play key roles in synchronization and transport processes. Synchronization is preceded by symmetry-breaking associated with double-resonance oscillations and is shown to be strongly dependent on the network size: convergence to the synchronization manifold occurs much faster with a large network. For small networks, increasing the noise level enhances synchronization in the weakly coupled regime, while particles in a large network are weakly synchronized. Similarly, in the strongly coupled regime, particles in a small network are weakly synchronized; whereas the synchronization is strong and robust against noise when the network-size is large. Small and moderate networks maximize and stabilize efficient transport. Although the dynamics for larger networks is highly correlated, the transport current is erratic.
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Affiliation(s)
- U E Vincent
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom.
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15
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Li R, Chu T. Complete synchronization of Boolean networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2012; 23:840-846. [PMID: 24806133 DOI: 10.1109/tnnls.2012.2190094] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We examine complete synchronization of two deterministic Boolean networks (BNs) coupled unidirectionally in the drive-response configuration. A necessary and sufficient criterion is presented in terms of algebraic representations of BNs. As a consequence, we show that complete synchronization can occur only between two conditionally identical BNs when the transition matrix of the drive network is nonsingular. Two examples are worked out to illustrate the obtained results.
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16
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Resmi V, Ambika G, Amritkar RE, Rangarajan G. Amplitude death in complex networks induced by environment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:046211. [PMID: 22680560 DOI: 10.1103/physreve.85.046211] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2012] [Indexed: 06/01/2023]
Abstract
We present a mechanism for amplitude death in coupled nonlinear dynamical systems on a complex network having interactions with a common environment like external system. We develop a general stability analysis that is valid for any network topology and obtain the threshold values of coupling constants for the onset of amplitude death. An important outcome of our study is a universal relation between the critical coupling strength and the largest nonzero eigenvalue of the coupling matrix. Our results are fully supported by the detailed numerical analysis for different network topologies.
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Affiliation(s)
- V Resmi
- Indian Institute of Science Education and Research, Pune 411021, India.
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17
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Tang G, Xu K, Jiang L. Synchronization in a chaotic neural network with time delay depending on the spatial distance between neurons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:046207. [PMID: 22181245 DOI: 10.1103/physreve.84.046207] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2011] [Revised: 06/11/2011] [Indexed: 05/31/2023]
Abstract
The synchronization is investigated in a two-dimensional Hindmarsh-Rose neuronal network by introducing a global coupling scheme with time delay, where the length of time delay is proportional to the spatial distance between neurons. We find that the time delay always disturbs synchronization of the neuronal network. When both the coupling strength and length of time delay per unit distance (i.e., enlargement factor) are large enough, the time delay induces the abnormal membrane potential oscillations in neurons. Specifically, the abnormal membrane potential oscillations for the symmetrically placed neurons form an antiphase, so that the large coupling strength and enlargement factor lead to the desynchronization of the neuronal network. The complete and intermittently complete synchronization of the neuronal network are observed for the right choice of parameters. The physical mechanism underlying these phenomena is analyzed.
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Affiliation(s)
- Guoning Tang
- College of Physics and Technology, Guangxi Normal University, Guilin 541004, China.
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18
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Resmi V, Ambika G, Amritkar RE. General mechanism for amplitude death in coupled systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:046212. [PMID: 22181250 DOI: 10.1103/physreve.84.046212] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2011] [Revised: 09/05/2011] [Indexed: 05/31/2023]
Abstract
We introduce a general mechanism for amplitude death in coupled synchronizable dynamical systems. It is known that when two systems are coupled directly, they can synchronize under suitable conditions. When an indirect feedback coupling through an environment or an external system is introduced in them, it is found to induce a tendency for antisynchronization. We show that, for sufficient strengths, these two competing effects can lead to amplitude death. We provide a general stability analysis that gives the threshold values for onset of amplitude death. We study in detail the nature of the transition to death in several specific cases and find that the transitions can be of two types--continuous and discontinuous. By choosing a variety of dynamics, for example, periodic, chaotic, hyperchaotic, and time-delay systems, we illustrate that this mechanism is quite general and works for different types of direct coupling, such as diffusive, replacement, and synaptic couplings, and for different damped dynamics of the environment.
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Affiliation(s)
- V Resmi
- Indian Institute of Science Education and Research, Pune 411021, India.
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Bhowmick SK, Ghosh D, Dana SK. Synchronization in counter-rotating oscillators. CHAOS (WOODBURY, N.Y.) 2011; 21:033118. [PMID: 21974653 DOI: 10.1063/1.3624943] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
An oscillatory system can have opposite senses of rotation, clockwise or anticlockwise. We present a general mathematical description of how to obtain counter-rotating oscillators from the definition of a dynamical system. A type of mixed synchronization emerges in counter-rotating oscillators under diffusive scalar coupling when complete synchronization and antisynchronization coexist in different state variables. We present numerical examples of limit cycle van der Pol oscillator and chaotic Rössler and Lorenz systems. Stability conditions of mixed synchronization are analytically obtained for both Rössler and Lorenz systems. Experimental evidences of counter-rotating limit cycle and chaotic oscillators and mixed synchronization are given in electronic circuits.
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Affiliation(s)
- Sourav K Bhowmick
- Central Instrumentation, Indian Institute of Chemical Biology (Council of Scientific and Industrial Research), Jadavpur, Kolkata 700032, India
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Xiwei Liu, Tianping Chen. Cluster Synchronization in Directed Networks Via Intermittent Pinning Control. ACTA ACUST UNITED AC 2011; 22:1009-20. [DOI: 10.1109/tnn.2011.2139224] [Citation(s) in RCA: 245] [Impact Index Per Article: 18.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Resmi V, Ambika G, Amritkar RE. Synchronized states in chaotic systems coupled indirectly through a dynamic environment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:046216. [PMID: 20481816 DOI: 10.1103/physreve.81.046216] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2009] [Revised: 02/15/2010] [Indexed: 05/29/2023]
Abstract
We consider synchronization of chaotic systems coupled indirectly through common environment where the environment has an intrinsic dynamics of its own modulated via feedback from the systems. We find that a rich variety of synchronization behavior, such as in-phase, antiphase, complete, and antisynchronization, is possible. We present an approximate stability analysis for the different synchronization behaviors. The transitions to different states of synchronous behavior are analyzed in the parameter plane of coupling strengths by numerical studies for specific cases such as Rössler and Lorenz systems and are characterized using various indices such as correlation, average phase difference, and Lyapunov exponents. The threshold condition obtained from numerical analysis is found to agree with that from the stability analysis.
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Affiliation(s)
- V Resmi
- Indian Institute of Science Education and Research, Pune 411021, India.
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