1
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Nag Chowdhury S, Anwar MS, Ghosh D. Cluster formation due to repulsive spanning trees in attractively coupled networks. Phys Rev E 2024; 109:044314. [PMID: 38755838 DOI: 10.1103/physreve.109.044314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2023] [Accepted: 03/22/2024] [Indexed: 05/18/2024]
Abstract
Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological processes. The current literature has investigated cluster synchronization by focusing mostly on the case of attractive coupling among the oscillators. However, the case of two coexisting competing interactions is of practical interest due to their relevance in diverse natural settings, including neuronal networks consisting of excitatory and inhibitory neurons, the coevolving social model with voters of opposite opinions, and ecological plant communities with both facilitation and competition, to name a few. In the present article, we investigate the impact of repulsive spanning trees on cluster formation within a connected network of attractively coupled limit-cycle oscillators. We successfully predict which nodes belong to each cluster and the emergent frustration of the connected networks independent of the particular local dynamics at the network nodes. We also determine local asymptotic stability of the cluster states using an approach based on the formulation of a master stability function. We additionally validate the emergence of solitary states and antisynchronization for some specific choices of spanning trees and networks.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, Davis, California 95616, USA
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Md Sayeed Anwar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
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2
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Abstract
Relay synchronization in multi-layer networks implies inter-layer synchronization between two indirectly connected layers through a relay layer. In this work, we study the relay synchronization in a three-layer multiplex network by introducing degree-based weighting mechanisms. The mechanism of within-layer connectivity may be hubs-repelling or hubs-attracting whenever low-degree or high-degree nodes receive strong influence. We adjust the remote layers to hubs-attracting coupling, whereas the relay layer may be unweighted, hubs-repelling, or hubs-attracting network. We establish that relay synchronization is improved when the relay layer is hubs-repelling compared to the other cases. We determine analytically necessary stability conditions of relay synchronization state using the master stability function approach. Finally, we explore the relation between synchronization and the topological property of the relay layer. We find that a higher clustering coefficient hinders synchronizability, and vice versa. We also look into the intra-layer synchronization in the proposed weighted triplex network and establish that intra-layer synchronization occurs in a wider range when relay layer is hubs-attracting.
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3
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Huang K, Sorrentino F, Hossein-Zadeh M. Experimental observations of synchronization between two bidirectionally coupled physically dissimilar oscillators. Phys Rev E 2020; 102:042215. [PMID: 33212708 DOI: 10.1103/physreve.102.042215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2020] [Accepted: 09/10/2020] [Indexed: 06/11/2023]
Abstract
We experimentally study the complex dynamics of two mutually coupled physically dissimilar oscillators with two different kinds of coupling mechanisms. Specifically, an optoelectronic oscillator is coupled to a Colpitts oscillator via optical power and the Colpitts oscillator is coupled back to the optoelectronic oscillator via electric voltage. We investigate and characterize phase synchronization and generalized chaos synchronization in this coupled system. Phase synchronization is observed when both oscillators are preset to oscillate periodically prior to coupling while generalized chaos synchronization is observed when both oscillators are preset to oscillate chaotically prior to coupling. In the periodical oscillation regime, we observe a linear relationship between the strengths of the two unidirectional coupling factors at which the system transitions to a synchronized state. In the chaotic regime, we observe a transition from hyperchaos to chaos associated with the onset of generalized synchronization.
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Affiliation(s)
- Ke Huang
- Center for High Technology Materials, The University of New Mexico, 1313 Goddard Street SE, Albuquerque, New Mexico 87106, USA
| | - Francesco Sorrentino
- Department of Mechanical Engineering, The University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Mani Hossein-Zadeh
- Center for High Technology Materials, The University of New Mexico, 1313 Goddard Street SE, Albuquerque, New Mexico 87106, USA
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4
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Rybalova E, Strelkova G, Schöll E, Anishchenko V. Relay and complete synchronization in heterogeneous multiplex networks of chaotic maps. CHAOS (WOODBURY, N.Y.) 2020; 30:061104. [PMID: 32611120 DOI: 10.1063/5.0008902] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Accepted: 05/21/2020] [Indexed: 06/11/2023]
Abstract
We study relay and complete synchronization in a heterogeneous triplex network of discrete-time chaotic oscillators. A relay layer and two outer layers, which are not directly coupled but interact via the relay layer, represent rings of nonlocally coupled two-dimensional maps. We consider for the first time the case when the spatiotemporal dynamics of the relay layer is completely different from that of the outer layers. Two different configurations of the triplex network are explored: when the relay layer consists of Lozi maps while the outer layers are given by Henon maps and vice versa. Phase and amplitude chimera states are observed in the uncoupled Henon map ring, while solitary state regimes are typical for the isolated Lozi map ring. We show for the first time relay synchronization of amplitude and phase chimeras, a solitary state chimera, and solitary state regimes in the outer layers. We reveal regimes of complete synchronization for the chimera structures and solitary state modes in all the three layers. We also analyze how the synchronization effects depend on the spatiotemporal dynamics of the relay layer and construct phase diagrams in the parameter plane of inter-layer vs intra-layer coupling strength of the relay layer.
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Affiliation(s)
- E Rybalova
- Department of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - G Strelkova
- Department of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - E Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - V Anishchenko
- Department of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
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5
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Rakshit S, Bera BK, Kurths J, Ghosh D. Enhancing synchrony in multiplex network due to rewiring frequency. Proc Math Phys Eng Sci 2019. [DOI: 10.1098/rspa.2019.0460] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Most of the previous studies on synchrony in multiplex networks have been investigated using different types of intralayer network architectures which are either static or temporal. Effect of a temporal layer on intralayer synchrony in a multilayered network still remains elusive. In this paper, we discuss intralayer synchrony in a multiplex network consisting of static and temporal layers and how a temporal layer influences other static layers to enhance synchrony simultaneously. We analytically derive local stability conditions for intralayer synchrony based on the master stability function approach. The analytically derived results are illustrated by numerical simulations on up to five-layers multiplex networks with the paradigmatic Lorenz system as the node dynamics in each individual layer.
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Affiliation(s)
- Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Bidesh K. Bera
- Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140001, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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6
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Karakaya B, Minati L, Gambuzza LV, Frasca M. Fading of remote synchronization in tree networks of Stuart-Landau oscillators. Phys Rev E 2019; 99:052301. [PMID: 31212500 DOI: 10.1103/physreve.99.052301] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Indexed: 11/07/2022]
Abstract
Remote synchronization (RS) is characterized by the appearance of phase coherence between oscillators that do not directly interact through a structural link in a network but exclusively through other units that are not synchronized or more weakly synchronized with them. This form of phase synchronization was observed initially in starlike motifs and later in random networks. In this paper, we report on an experimental setup for the analysis of RS in networks of Stuart-Landau oscillators and in particular investigate the behavior of tree structures focusing on the path to synchronization, that is, on the analysis of how synchronization emerges as the coupling strength increases from zero. We find that RS occurs in a region wherein further increases of the coupling strength lead to a direct transition to global synchronization but may also be observed in a second region, corresponding to lower coupling values, wherein it first emerges and then disappears, hallmarking a scenario that we denote as fading of remote synchronization. We show that this result is related to the behavior of pairs of remotely synchronized nodes observed in networks with more general topologies. Experiments are corroborated by numerical simulations confirming the major findings and providing further characterization of the phenomenon. We demonstrate that the distribution of natural oscillation frequencies and the parameter uncertainty in the links both play a fundamental role in shaping the behaviors observed.
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Affiliation(s)
- Baris Karakaya
- Faculty of Engineering, Department of Electrical, Electronics Engineering, Firat University, 23119 Elazig, Turkey
| | - Ludovico Minati
- World Research Hub Initiative-Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8503, Japan; Complex Systems Theory Department, Institute of Nuclear Physics-Polish Academy of Sciences (IFJ-PAN), 31-342 Kraków, Poland; and Center for Mind/Brain Sciences (CIMeC), University of Trento, 38123 Trento, Italy
| | - Lucia Valentina Gambuzza
- Dipartimento Ingegneria Elettrica Elettronica e Informatica, Università degli Studi di Catania, 95029 Catania, Italy
| | - Mattia Frasca
- Dipartimento Ingegneria Elettrica Elettronica e Informatica, Università degli Studi di Catania, 95029 Catania, Italy.,CNR-IASI, Italian National Research Council-Institute for Systems Analysis and Computer Science "A. Ruberti," 00185 Rome, Italy
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7
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Bolotov MI, Munyaev VO, Kryukov AK, Smirnov LA, Osipov GV. Variety of rotation modes in a small chain of coupled pendulums. CHAOS (WOODBURY, N.Y.) 2019; 29:033109. [PMID: 30927845 DOI: 10.1063/1.5079499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2018] [Accepted: 02/11/2019] [Indexed: 06/09/2023]
Abstract
This article studies the rotational dynamics of three identical coupled pendulums. There exist two parameter areas where the in-phase rotational motion is unstable and out-of-phase rotations are realized. Asymptotic theory is developed that allows us to analytically identify borders of instability areas of in-phase rotation motion. It is shown that out-of-phase rotations are the result of the parametric instability of in-phase motion. Complex out-of-phase rotations are numerically found and their stability and bifurcations are defined. It is demonstrated that the emergence of chaotic dynamics happens due to the period doubling bifurcation cascade. The detailed scenario of symmetry breaking is presented. The development of chaotic dynamics leads to the origin of two chaotic attractors of different types. The first one is characterized by the different phases of all pendulums. In the second case, the phases of the two pendulums are equal, and the phase of the third one is different. This regime can be interpreted as a drum-head mode in star-networks. It may also indicate the occurrence of chimera states in chains with a greater number of nearest-neighbour interacting elements and in analogical systems with global coupling.
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Affiliation(s)
- Maxim I Bolotov
- Department of Control Theory, Nizhny Novgorod State University, Gagarin Ave. 23, Nizhny Novgorod 603950, Russia
| | - Vyacheslav O Munyaev
- Department of Control Theory, Nizhny Novgorod State University, Gagarin Ave. 23, Nizhny Novgorod 603950, Russia
| | - Alexey K Kryukov
- Department of Control Theory, Nizhny Novgorod State University, Gagarin Ave. 23, Nizhny Novgorod 603950, Russia
| | - Lev A Smirnov
- Department of Control Theory, Nizhny Novgorod State University, Gagarin Ave. 23, Nizhny Novgorod 603950, Russia
| | - Grigory V Osipov
- Department of Control Theory, Nizhny Novgorod State University, Gagarin Ave. 23, Nizhny Novgorod 603950, Russia
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8
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Majhi S, Muruganandam P, Ferreira FF, Ghosh D, Dana SK. Asymmetry in initial cluster size favors symmetry in a network of oscillators. CHAOS (WOODBURY, N.Y.) 2018; 28:081101. [PMID: 30180614 DOI: 10.1063/1.5043588] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2018] [Accepted: 07/13/2018] [Indexed: 06/08/2023]
Abstract
Counterintuitive to the common notion of symmetry breaking, asymmetry favors synchrony in a network of oscillators. Our observations on an ensemble of identical Stuart-Landau systems under a symmetry breaking coupling support our conjecture. As usual, for a complete deterministic and the symmetric choice of initial clusters, a variety of asymptotic states, namely, multicluster oscillation death (1-OD, 3-OD, and m -OD), chimera states, and traveling waves emerge. Alternatively, multiple chimera death (1-CD, 3-CD, and m -CD) and completely synchronous states emerge in the network whenever some randomness is added to the symmetric initial states. However, in both the cases, an increasing asymmetry in the initial cluster size restores symmetry in the network, leading to the most favorable complete synchronization state for a broad range of coupling parameters. We are able to reduce the network model using the mean-field approximation that reproduces the dynamical features of the original network.
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Affiliation(s)
- Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - P Muruganandam
- Department of Physics, Barathidasan University, Tiruchirapalli 620024, India
| | - F F Ferreira
- Center for Interdisciplinary Research in Complex Systems, University of São Paulo, São Paulo, São Paulo 03828-000, Brazil
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Syamal K Dana
- Department of Mathematics, Jadavpur University, Kolkata 700032, India
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9
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Leyva I, Sendiña-Nadal I, Sevilla-Escoboza R, Vera-Avila VP, Chholak P, Boccaletti S. Relay synchronization in multiplex networks. Sci Rep 2018; 8:8629. [PMID: 29872135 PMCID: PMC5988811 DOI: 10.1038/s41598-018-26945-w] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2018] [Accepted: 05/21/2018] [Indexed: 11/09/2022] Open
Abstract
Relay (or remote) synchronization between two not directly connected oscillators in a network is an important feature allowing distant coordination. In this work, we report a systematic study of this phenomenon in multiplex networks, where inter-layer synchronization occurs between distant layers mediated by a relay layer that acts as a transmitter. We show that this transmission can be extended to higher order relay configurations, provided symmetry conditions are preserved. By first order perturbative analysis, we identify the dynamical and topological dependencies of relay synchronization in a multiplex. We find that the relay synchronization threshold is considerably reduced in a multiplex configuration, and that such synchronous state is mostly supported by the lower degree nodes of the outer layers, while hubs can be de-multiplexed without affecting overall coherence. Finally, we experimentally validated the analytical and numerical findings by means of a multiplex of three layers of electronic circuits.
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Affiliation(s)
- I Leyva
- Complex Systems Group & GISC, Universidad Rey Juan Carlos, Móstoles, Madrid, 28933, Spain.
- Center for Biomedical Technology, Universidad Politécnica de Madrid, Pozuelo de Alarcón, Madrid, 28223, Spain.
| | - I Sendiña-Nadal
- Complex Systems Group & GISC, Universidad Rey Juan Carlos, Móstoles, Madrid, 28933, Spain
- Center for Biomedical Technology, Universidad Politécnica de Madrid, Pozuelo de Alarcón, Madrid, 28223, Spain
| | - R Sevilla-Escoboza
- Centro Universitario de los Lagos, Universidad de Guadalajara, Jalisco, 47460, Mexico
| | - V P Vera-Avila
- Centro Universitario de los Lagos, Universidad de Guadalajara, Jalisco, 47460, Mexico
| | - P Chholak
- Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India
| | - S Boccaletti
- CNR-Institute of complex systems, Via Madonna del Piano 10, Sesto Fiorentino, 50019, Italy
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10
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Montaseri G, Meyer-Hermann M. Diversity of coupled oscillators can enhance their synchronization. Phys Rev E 2016; 94:042213. [PMID: 27841630 DOI: 10.1103/physreve.94.042213] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2016] [Indexed: 11/07/2022]
Abstract
The heterogeneity of coupled oscillators is important for the degree of their synchronization. According to the classical Kuramoto model, larger heterogeneity reduces synchronization. Here, we show that in a model for coupled pancreatic β-cells, higher diversity of the cells induces higher synchrony. We find that any system of coupled oscillators that oscillates on two time scales and in which heterogeneity causes a transition from chaotic to damped oscillations on the fast time scale exhibits this property. Thus, synchronization of a subset of oscillating systems can be enhanced by increasing the heterogeneity of the system constituents.
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Affiliation(s)
- Ghazal Montaseri
- Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Braunschweig 38124, Germany
| | - Michael Meyer-Hermann
- Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Braunschweig 38124, Germany.,Institute for Biochemistry, Biotechnology and Bioinformatics, Technische Universität Braunschweig, Braunschweig 38106, Germany
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11
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Gambuzza LV, Frasca M, Fortuna L, Boccaletti S. Inhomogeneity induces relay synchronization in complex networks. Phys Rev E 2016; 93:042203. [PMID: 27176289 DOI: 10.1103/physreve.93.042203] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2015] [Indexed: 11/07/2022]
Abstract
Relay synchronization is a collective state, originally found in chains of interacting oscillators, in which uncoupled dynamical units synchronize through the action of mismatched inner nodes that relay the information but do not synchronize with them. It is demonstrated herein that relay synchronization is not limited to such simple motifs, rather it can emerge in larger and arbitrary network topologies. In particular, we show how this phenomenon can be observed in networks of chaotic systems in the presence of some mismatched units, the relay nodes, and how it is actually responsible for an enhancement of synchronization in the network.
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Affiliation(s)
| | - Mattia Frasca
- DIEEI, Università degli Studi di Catania, Catania, Italy
| | - Luigi Fortuna
- DIEEI, Università degli Studi di Catania, Catania, Italy
| | - Stefano Boccaletti
- CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.,The Embassy of Italy in Tel Aviv, 25 Hamered Street, 68125 Tel Aviv, Israel
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12
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Padmanaban E, Saha S, Vigneshwaran M, Dana SK. Amplified response in coupled chaotic oscillators by induced heterogeneity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062916. [PMID: 26764783 DOI: 10.1103/physreve.92.062916] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2015] [Indexed: 06/05/2023]
Abstract
The phenomenon of emergent amplified response is reported in two unidirectionally coupled identical chaotic systems when heterogeneity as a parameter mismatch is introduced in a state of complete synchrony. The amplified response emerges from the interplay of heterogeneity and a type of cross-feedback coupling. It is reflected as an expansion of the response attractor in some directions in the state space of the coupled system. The synchronization manifold is simply rotated by the parameter detuning while its stability in the transverse direction is still maintained. The amplification factor is linearly related to the amount of parameter detuning. The phenomenon is elaborated with examples of the paradigmatic Lorenz system, the Shimizu-Morioka single-mode laser model, the Rössler system, and a Sprott system. Experimental evidence of the phenomenon is obtained in an electronic circuit. The method may provide an engineering tool for distortion-free amplification of chaotic signals.
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Affiliation(s)
- E Padmanaban
- CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032, India
| | - Suman Saha
- CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032, India
| | - M Vigneshwaran
- CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032, India
| | - Syamal K Dana
- CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032, India
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13
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Ghasemi Esfahani Z, Valizadeh A. Zero-lag synchronization despite inhomogeneities in a relay system. PLoS One 2014; 9:e112688. [PMID: 25486522 PMCID: PMC4259331 DOI: 10.1371/journal.pone.0112688] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2014] [Accepted: 10/10/2014] [Indexed: 11/18/2022] Open
Abstract
A novel proposal for the zero-lag synchronization of the delayed coupled neurons, is to connect them indirectly via a third relay neuron. In this study, we develop a Poincaré map to investigate the robustness of the synchrony in such a relay system against inhomogeneity in the neurons and synaptic parameters. We show that when the inhomogeneity does not violate the symmetry of the system, synchrony is maintained and in some cases inhomogeneity enhances synchrony. On the other hand if the inhomogeneity breaks the symmetry of the system, zero lag synchrony can not be preserved. In this case we give analytical results for the phase lag of the spiking of the neurons in the stable state.
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14
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Sharma A, Shrimali MD, Aihara K. Effect of mixed coupling on relay-coupled Rössler and Lorenz oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062907. [PMID: 25615164 DOI: 10.1103/physreve.90.062907] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2014] [Indexed: 06/04/2023]
Abstract
The complete synchronization between the outermost oscillators using the mixed coupling in relay coupled systems is studied. Mixed coupling has two types of coupling functions: coupling between similar or dissimilar variables. We examine the complete synchronization in relay-coupled systems by the largest transverse Lyapunov exponent and synchronization error. We show numerically for Rössler and Lorenz oscillators that the combination of these two types of coupling functions is able to decrease the critical coupling strength for complete synchronization as well as it also suppress oscillations for larger coupling strength.
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Affiliation(s)
- Amit Sharma
- FIRST, Aihara Innovative Mathematical Modelling Project, Japan Science and Technology Agency, Meguro-ku, Tokyo 153-8505, Japan
| | - Manish Dev Shrimali
- Department of Physics, Central University of Rajasthan, NH-8, Bandar Sindri, Ajmer 305 817, India
| | - K Aihara
- FIRST, Aihara Innovative Mathematical Modelling Project, Japan Science and Technology Agency, Meguro-ku, Tokyo 153-8505, Japan and Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
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15
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Mechanisms of zero-lag synchronization in cortical motifs. PLoS Comput Biol 2014; 10:e1003548. [PMID: 24763382 PMCID: PMC3998884 DOI: 10.1371/journal.pcbi.1003548] [Citation(s) in RCA: 90] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2013] [Accepted: 02/20/2014] [Indexed: 12/04/2022] Open
Abstract
Zero-lag synchronization between distant cortical areas has been observed in a diversity of experimental data sets and between many different regions of the brain. Several computational mechanisms have been proposed to account for such isochronous synchronization in the presence of long conduction delays: Of these, the phenomenon of “dynamical relaying” – a mechanism that relies on a specific network motif – has proven to be the most robust with respect to parameter mismatch and system noise. Surprisingly, despite a contrary belief in the community, the common driving motif is an unreliable means of establishing zero-lag synchrony. Although dynamical relaying has been validated in empirical and computational studies, the deeper dynamical mechanisms and comparison to dynamics on other motifs is lacking. By systematically comparing synchronization on a variety of small motifs, we establish that the presence of a single reciprocally connected pair – a “resonance pair” – plays a crucial role in disambiguating those motifs that foster zero-lag synchrony in the presence of conduction delays (such as dynamical relaying) from those that do not (such as the common driving triad). Remarkably, minor structural changes to the common driving motif that incorporate a reciprocal pair recover robust zero-lag synchrony. The findings are observed in computational models of spiking neurons, populations of spiking neurons and neural mass models, and arise whether the oscillatory systems are periodic, chaotic, noise-free or driven by stochastic inputs. The influence of the resonance pair is also robust to parameter mismatch and asymmetrical time delays amongst the elements of the motif. We call this manner of facilitating zero-lag synchrony resonance-induced synchronization, outline the conditions for its occurrence, and propose that it may be a general mechanism to promote zero-lag synchrony in the brain. Understanding large-scale neuronal dynamics – and how they relate to the cortical anatomy – is one of the key areas of neuroscience research. Despite a wealth of recent research, the key principles of this relationship have yet to be established. Here we employ computational modeling to study neuronal dynamics on small subgraphs – or motifs – across a hierarchy of spatial scales. We establish a novel organizing principle that we term a “resonance pair” (two mutually coupled nodes), which promotes stable, zero-lag synchrony amongst motif nodes. The bidirectional coupling between a resonance pair acts to mutually adjust their dynamics onto a common and relatively stable synchronized regime, which then propagates and stabilizes the synchronization of other nodes within the motif. Remarkably, we find that this effect can propagate along chains of coupled nodes and hence holds the potential to promote stable zero-lag synchrony in larger sub-networks of cortical systems. Our findings hence suggest a potential unifying account of the existence of zero-lag synchrony, an important phenomenon that may underlie crucial cognitive processes in the brain. Moreover, such pairs of mutually coupled oscillators are found in a wide variety of physical and biological systems suggesting a new, broadly relevant and unifying principle.
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16
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Gutiérrez R, Sevilla-Escoboza R, Piedrahita P, Finke C, Feudel U, Buldú JM, Huerta-Cuellar G, Jaimes-Reátegui R, Moreno Y, Boccaletti S. Generalized synchronization in relay systems with instantaneous coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052908. [PMID: 24329332 DOI: 10.1103/physreve.88.052908] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2013] [Revised: 09/23/2013] [Indexed: 06/03/2023]
Abstract
We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it.
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Affiliation(s)
- R Gutiérrez
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - R Sevilla-Escoboza
- Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco 47460, Mexico and Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
| | - P Piedrahita
- Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50009, Spain
| | - C Finke
- d-fine GmbH, Opernplatz 2, 60313 Frankfurt, Germany
| | - U Feudel
- ICBM, University of Oldenburg, Carl-von-Ossietzky-Strasse 9-11, 26111 Oldenburg, Germany and IPST, University of Maryland, College Park, Maryland 20742-2431, USA
| | - J M Buldú
- Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain and Center for Biomedical Technology, Technical University of Madrid, Pozuelo de Alarcón, 28223 Madrid, Spain
| | - G Huerta-Cuellar
- Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco 47460, Mexico
| | - R Jaimes-Reátegui
- Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco 47460, Mexico
| | - Y Moreno
- Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50009, Spain and Department of Theoretical Physics, University of Zaragoza, Zaragoza 50009, Spain and Complex Networks and Systems Lagrange Lab, Institute for Scientific Interchange, Turin, Italy
| | - S Boccaletti
- CNR Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy
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