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Irankhah R, Mehrabbeik M, Parastesh F, Rajagopal K, Jafari S, Kurths J. Synchronization enhancement subjected to adaptive blinking coupling. CHAOS (WOODBURY, N.Y.) 2024; 34:023120. [PMID: 38377293 DOI: 10.1063/5.0188366] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Accepted: 01/25/2024] [Indexed: 02/22/2024]
Abstract
Synchronization holds a significant role, notably within chaotic systems, in various contexts where the coordinated behavior of systems plays a pivotal and indispensable role. Hence, many studies have been dedicated to investigating the underlying mechanism of synchronization of chaotic systems. Networks with time-varying coupling, particularly those with blinking coupling, have been proven essential. The reason is that such coupling schemes introduce dynamic variations that enhance adaptability and robustness, making them applicable in various real-world scenarios. This paper introduces a novel adaptive blinking coupling, wherein the coupling adapts dynamically based on the most influential variable exhibiting the most significant average disparity. To ensure an equitable selection of the most effective coupling at each time instance, the average difference of each variable is normalized to the synchronous solution's range. Due to this adaptive coupling selection, synchronization enhancement is expected to be observed. This hypothesis is assessed within networks of identical systems, encompassing Lorenz, Rössler, Chen, Hindmarsh-Rose, forced Duffing, and forced van der Pol systems. The results demonstrated a substantial improvement in synchronization when employing adaptive blinking coupling, particularly when applying the normalization process.
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Affiliation(s)
- Reza Irankhah
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, Iran
| | - Mahtab Mehrabbeik
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, Iran
| | - Fatemeh Parastesh
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, Iran
- Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, Iran
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
- Institute of Physics, Humboldt University of Berlin, Berlin 12489, Germany
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Tang L, Smith K, Daley K, Belykh I. When multilayer links exchange their roles in synchronization. Phys Rev E 2022; 106:024214. [PMID: 36109922 DOI: 10.1103/physreve.106.024214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2022] [Accepted: 08/09/2022] [Indexed: 06/15/2023]
Abstract
Real world networks contain multiple layers of links whose interactions can lead to extraordinary collective dynamics, including synchronization. The fundamental problem of assessing how network topology controls synchronization in multilayer networks remains open due to serious limitations of the existing stability methods. Towards removing this obstacle, we propose an approximation method which significantly enhances the predictive power of the master stability function for stable synchronization in multilayer networks. For a class of saddle-focus oscillators, including Rössler and piecewise linear systems, our method reduces the complex stability analysis to simply solving a set of linear algebraic equations. Using the method, we analytically predict surprising effects due to multilayer coupling. In particular, we prove that two coupling layers-one of which would alone hamper synchronization and the other would foster it-reverse their roles when used in a multilayer network. We also analytically demonstrate that increasing the size of a globally coupled layer, that in isolation would induce stable synchronization, makes the multilayer network unsynchronizable.
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Affiliation(s)
- Longkun Tang
- School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
- Department of Mathematics and Statistics, Georgia State University, P.O. Box 4110, Atlanta, Georgia 30302-410, USA
| | - Kelley Smith
- Department of Mathematics and Statistics, Georgia State University, P.O. Box 4110, Atlanta, Georgia 30302-410, USA
| | - Kevin Daley
- Department of Mathematics and Statistics, Georgia State University, P.O. Box 4110, Atlanta, Georgia 30302-410, USA
| | - Igor Belykh
- Department of Mathematics and Statistics, Georgia State University, P.O. Box 4110, Atlanta, Georgia 30302-410, USA
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Singla T, Rivera M. Explosive synchronization in temporal networks: A comparative study. CHAOS (WOODBURY, N.Y.) 2020; 30:113135. [PMID: 33261337 DOI: 10.1063/5.0023329] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2020] [Accepted: 10/29/2020] [Indexed: 06/12/2023]
Abstract
We present a comparative study on Explosive Synchronization (ES) in temporal networks consisting of phase oscillators. The temporal nature of the networks is modeled with two configurations: (1) oscillators are allowed to move in a closed two-dimensional box such that they couple with their neighbors and (2) oscillators are static and they randomly switch their coupling partners. Configuration (1) is further studied under two possible scenarios: in the first case, oscillators couple to fixed numbers of neighbors, while, in the other case, they couple to all oscillators lying in their circle of vision. Under these circumstances, we monitor the degrees of temporal networks, velocities, and radius of circle of vision of the oscillators and the probability of forming connections in order to study and compare the critical values of the coupling required to induce ES in the population of phase oscillators.
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Affiliation(s)
- Tanu Singla
- Tecnológico de Monterrey, Calle del Puente 222, Colonia Ejidos de Huipulco, Tlalpan, Ciudad de México 14380, México
| | - M Rivera
- Centro de Investigación en Ciencias (IICBA), UAEM, Avenida Universidad 1001, Colonia Chamilpa, Cuernavaca, Morelos 62209, México
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He Z, Yao C, Yu J, Zhan M. Perturbation analysis and comparison of network synchronization methods. Phys Rev E 2019; 99:052207. [PMID: 31212531 DOI: 10.1103/physreve.99.052207] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Indexed: 11/07/2022]
Abstract
In many networked systems, synchronization is important and useful, and how to enhance synchronizability is an interesting problem. Based on the matrix perturbation theory, we analyze five methods of network synchronization enhancement, including the link removal, node removal, dividing hub node, pull control, and pinning control methods, and obtain explicit expressions for eigenvalue changes. By these comparisons, we find that, among all these methods, the pull control method is remarkable, as it can extend the synchronization (coupling strength) region from both the left and right sides, for any controlled node. Extensive simulation results are given to support the accuracy of the perturbation-based analysis.
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Affiliation(s)
- Zhiwei He
- Department of Mathematics, Shaoxing University, Shaoxing 312000, China
| | - Chenggui Yao
- Department of Mathematics, Shaoxing University, Shaoxing 312000, China
| | - Jun Yu
- Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China
| | - Meng Zhan
- State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
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Fan H, Wang Y, Wang H, Lai YC, Wang X. Autapses promote synchronization in neuronal networks. Sci Rep 2018; 8:580. [PMID: 29330551 PMCID: PMC5766500 DOI: 10.1038/s41598-017-19028-9] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2017] [Accepted: 12/20/2017] [Indexed: 11/09/2022] Open
Abstract
Neurological disorders such as epileptic seizures are believed to be caused by neuronal synchrony. However, to ascertain the causal role of neuronal synchronization in such diseases through the traditional approach of electrophysiological data analysis remains a controversial, challenging, and outstanding problem. We offer an alternative principle to assess the physiological role of neuronal synchrony based on identifying structural anomalies in the underlying network and studying their impacts on the collective dynamics. In particular, we focus on autapses - time delayed self-feedback links that exist on a small fraction of neurons in the network, and investigate their impacts on network synchronization through a detailed stability analysis. Our main finding is that the proper placement of a small number of autapses in the network can promote synchronization significantly, providing the computational and theoretical bases for hypothesizing a high degree of synchrony in real neuronal networks with autapses. Our result that autapses, the shortest possible links in any network, can effectively modulate the collective dynamics provides also a viable strategy for optimal control of complex network dynamics at minimal cost.
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Affiliation(s)
- Huawei Fan
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710062, China
| | - Yafeng Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710062, China
| | - Hengtong Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710062, China
| | - Ying-Cheng Lai
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710062, China.,School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona, 85287, USA
| | - Xingang Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710062, China.
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Tang L, Wu X, Lü J, Lu JA. Bifurcation behaviors of synchronized regions in logistic map networks with coupling delay. CHAOS (WOODBURY, N.Y.) 2015; 25:033101. [PMID: 25833423 DOI: 10.1063/1.4913854] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Network synchronized regions play an extremely important role in network synchronization according to the master stability function framework. This paper focuses on network synchronous state stability via studying the effects of nodal dynamics, coupling delay, and coupling way on synchronized regions in Logistic map networks. Theoretical and numerical investigations show that (1) network synchronization is closely associated with its nodal dynamics. Particularly, the synchronized region bifurcation points through which the synchronized region switches from one type to another are in good agreement with those of the uncoupled node system, and chaotic nodal dynamics can greatly impede network synchronization. (2) The coupling delay generally impairs the synchronizability of Logistic map networks, which is also dominated by the parity of delay for some nodal parameters. (3) A simple nonlinear coupling facilitates network synchronization more than the linear one does. The results found in this paper will help to intensify our understanding for the synchronous state stability in discrete-time networks with coupling delay.
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Affiliation(s)
- Longkun Tang
- School of Mathematical Science, Huaqiao University, Quanzhou 362021, China
| | - Xiaoqun Wu
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
| | - Jinhu Lü
- LSC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
| | - Jun-An Lu
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
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Huang L, Chen Q, Lai YC, Pecora LM. Generic behavior of master-stability functions in coupled nonlinear dynamical systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:036204. [PMID: 19905197 DOI: 10.1103/physreve.80.036204] [Citation(s) in RCA: 84] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2009] [Indexed: 05/28/2023]
Abstract
Master-stability functions (MSFs) are fundamental to the study of synchronization in complex dynamical systems. For example, for a coupled oscillator network, a necessary condition for synchronization to occur is that the MSF at the corresponding normalized coupling parameters be negative. To understand the typical behaviors of the MSF for various chaotic oscillators is key to predicting the collective dynamics of a network of these oscillators. We address this issue by examining, systematically, MSFs for known chaotic oscillators. Our computations and analysis indicate that it is generic for MSFs being negative in a finite interval of a normalized coupling parameter. A general scheme is proposed to classify the typical behaviors of MSFs into four categories. These results are verified by direct simulations of synchronous dynamics on networks of actual coupled oscillators.
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Affiliation(s)
- Liang Huang
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
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Chen G, Duan Z. Network synchronizability analysis: a graph-theoretic approach. CHAOS (WOODBURY, N.Y.) 2008; 18:037102. [PMID: 19045476 DOI: 10.1063/1.2965530] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
This paper addresses the fundamental problem of complex network synchronizability from a graph-theoretic approach. First, the existing results are briefly reviewed. Then, the relationships between the network synchronizability and network structural parameters (e.g., average distance, degree distribution, and node betweenness centrality) are discussed. The effects of the complementary graph of a given network and some graph operations on the network synchronizability are discussed. A basic theory based on subgraphs and complementary graphs for estimating the network synchronizability is established. Several examples are given to show that adding new edges to a network can either increase or decrease the network synchronizability. To that end, some new results on the estimations of the synchronizability of coalescences are reported. Moreover, a necessary and sufficient condition for a network and its complementary network to have the same synchronizability is derived. Finally, some examples on Chua circuit networks are presented for illustration.
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Affiliation(s)
- Guanrong Chen
- State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, People's Republic of China.
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Funato T, Kurabayashi D, Nara M, Aonuma H. Switching mechanism of sensor-motor coordination through an oscillator network model. ACTA ACUST UNITED AC 2008; 38:764-70. [PMID: 18558540 DOI: 10.1109/tsmcb.2008.922060] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Insects have small brains, but their behavior is highly adaptive; this leads us to conclude that their brains possess a simple adaptation mechanism. This paper focuses on the pheromone processing of crickets, varying their aggression depending on their global neural connection, and proposes a behavior selection mechanism that can be controlled by network transformation. The controller is composed of an oscillator network, and its behavior is decided by the synchrony of organic oscillations. Furthermore, every network component corresponds to a certain brain module. A model is realized by using an analog circuit, and it is applied to a simple robot that displays the behavior of a real insect.
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Affiliation(s)
- Tetsuro Funato
- Department of Mechanicaland Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan.
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Perlikowski P, Jagiello B, Stefanski A, Kapitaniak T. Experimental observation of ragged synchronizability. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:017203. [PMID: 18764084 DOI: 10.1103/physreve.78.017203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2008] [Revised: 05/12/2008] [Indexed: 05/26/2023]
Abstract
Synchronization thresholds of an array of nondiagonally coupled oscillators are investigated. We present experimental results which show the existence of ragged synchronizability, i.e., the existence of multiple disconnected synchronization regions in the coupling parameter space. This phenomenon has been observed in an electronic implementation of an array of nondiagonally coupled van der Pol's oscillators. Numerical simulations show good agreement with the experimental observations.
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Affiliation(s)
- P Perlikowski
- Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland
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Duan Z, Chen G, Huang L. Complex network synchronizability: analysis and control. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:056103. [PMID: 18233714 DOI: 10.1103/physreve.76.056103] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2007] [Indexed: 05/25/2023]
Abstract
In this paper, the investigation is first motivated by showing two examples of simple regular symmetrical graphs, which have the same structural parameters, such as average distance, degree distribution, and node betweenness centrality, but have very different synchronizabilities. For a given network with identical node dynamics, it is further shown that two key factors influencing the network synchronizability are the network inner linking matrix and the eigenvalues of the network topological matrix. Several examples are then provided to show that adding new edges to a network can either increase or decrease the network synchronizability. In searching for conditions under which the network synchronizability may be increased by adding edges, it is found that for networks with disconnected complementary graphs, adding edges never decreases their synchronizability. Moreover, it is found that an unbounded synchronized region is always easier to analyze than a bounded synchronized region. Therefore to effectively enhance the network synchronizability, a design method is finally presented for the inner linking matrix of rank 1 such that the resultant network has an unbounded synchronized region, for the case where the synchronous state is an equilibrium point of the network.
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Affiliation(s)
- Zhisheng Duan
- State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, People's Republic of China.
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