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Dixit S, Aravind M, Parmananda P. Regulating dynamics through intermittent interactions. Phys Rev E 2022; 106:014203. [PMID: 35974523 DOI: 10.1103/physreve.106.014203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 05/23/2022] [Indexed: 06/15/2023]
Abstract
In this article we experimentally demonstrate an efficient scheme to regulate the behavior of coupled nonlinear oscillators through dynamic control of their interaction. It is observed that introducing intermittency in the interaction term as a function of time or the system state predictably alters the dynamics of the constituent oscillators. Choosing the nature of the interaction, attractive or repulsive, allows for either suppression of oscillations or stimulation of activity. Two parameters Δ and τ, that reign the extent of interaction among subsystems, are introduced. They serve as a harness to access the entire range of possible behaviors from fixed points to chaos. For fixed values of system parameters and coupling strength, changing Δ and τ offers fine control over the dynamics of coupled subsystems. We show this experimentally using coupled Chua's circuits and elucidate their behavior for a range of coupling parameters through detailed numerical simulations.
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Affiliation(s)
- Shiva Dixit
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Manaoj Aravind
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
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Premraj D, Suresh K, Thamilmaran K. Effect of processing delay on bifurcation delay in a network of slow-fast oscillators. CHAOS (WOODBURY, N.Y.) 2019; 29:123127. [PMID: 31893660 DOI: 10.1063/1.5123417] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2019] [Accepted: 12/04/2019] [Indexed: 06/10/2023]
Abstract
Bifurcation delay or slow passage effect occurs in dynamical systems with slow-fast time-varying parameters. In this work, we report the impact of processing delay on bifurcation delay in a network of locally coupled slow-fast systems with self-feedback delay. We report that the network exhibits coexisting coherent (synchronized) and incoherent (desynchronized) states among the oscillators as a function of various parameters like self-feedback delay, processing delay, and amplitude of the external current. In particular, we show the decrease of the synchronized region (control of synchronization) for (i) a fixed value of processing delay with varying self-feedback delay and (ii) fixed self-feedback delay with increasing processing delay. In contrast, we observe the increase of the synchronized region (control of desynchronization) for fixed processing delay and self-feedback delay while varying the amplitude of the external current. Finally, we have also analyzed the effect of processing delay on bifurcation delay with the presence of noise and we report that the inhomogeneity in the additional noise does not affect the asymmetry in a bifurcation delay.
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Affiliation(s)
- D Premraj
- Department of Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India
| | - K Suresh
- Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India
| | - K Thamilmaran
- Department of Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India
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Kundu P, Sharma L, Nandan M, Ghosh D, Hens C, Pal P. Emergent dynamics in delayed attractive-repulsively coupled networks. CHAOS (WOODBURY, N.Y.) 2019; 29:013112. [PMID: 30709156 DOI: 10.1063/1.5051535] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2018] [Accepted: 12/26/2018] [Indexed: 06/09/2023]
Abstract
We investigate different emergent dynamics, namely, oscillation quenching and revival of oscillation, in a global network of identical oscillators coupled with diffusive (positive) delay coupling as it is perturbed by symmetry breaking localized repulsive delayed interaction. Starting from the oscillatory state (OS), we systematically identify three types of transition phenomena in the parameter space: (1) The system may reach inhomogeneous steady states from the homogeneous steady state sometimes called as the transition from amplitude death (AD) to oscillation death (OD) state, i.e., OS-AD-OD scenario, (2) Revival of oscillation (OS) from the AD state (OS-AD-OS), and (3) Emergence of the OD state from the oscillatory state (OS) without passing through AD, i.e., OS-OD. The dynamics of each node in the network is assumed to be governed either by the identical limit cycle Stuart-Landau system or by the chaotic Rössler system. Based on clustering behavior observed in the oscillatory network, we derive a reduced low-dimensional model of the large network. Using the reduced model, we investigate the effect of time delay on these transitions and demarcate OS, AD, and OD regimes in the parameter space. We also explore and characterize the bifurcation transitions present in both systems. The generic behavior of the low dimensional model and full network is found to match satisfactorily.
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Affiliation(s)
- Prosenjit Kundu
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - Lekha Sharma
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | | | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Pinaki Pal
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
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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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Sun Z, Xiao R, Yang X, Xu W. Quenching oscillating behaviors in fractional coupled Stuart-Landau oscillators. CHAOS (WOODBURY, N.Y.) 2018; 28:033109. [PMID: 29604642 DOI: 10.1063/1.5019772] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Oscillation quenching has been widely studied during the past several decades in fields ranging from natural sciences to engineering, but investigations have so far been restricted to oscillators with an integer-order derivative. Here, we report the first study of amplitude death (AD) in fractional coupled Stuart-Landau oscillators with partial and/or complete conjugate couplings to explore oscillation quenching patterns and dynamics. It has been found that the fractional-order derivative impacts the AD state crucially. The area of the AD state increases along with the decrease of the fractional-order derivative. Furthermore, by introducing and adjusting a limiting feedback factor in coupling links, the AD state can be well tamed in fractional coupled oscillators. Hence, it provides one an effective approach to analyze and control the oscillating behaviors in fractional coupled oscillators.
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Affiliation(s)
- Zhongkui Sun
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China
| | - Rui Xiao
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China
| | - Xiaoli Yang
- College of Mathematics and Information Science, Shaan'xi Normal University, Xi'an 710062, People's Republic of China
| | - Wei Xu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China
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Teki H, Konishi K, Hara N. Amplitude death in a pair of one-dimensional complex Ginzburg-Landau systems coupled by diffusive connections. Phys Rev E 2017; 95:062220. [PMID: 28709208 DOI: 10.1103/physreve.95.062220] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2017] [Indexed: 11/07/2022]
Abstract
This paper shows that, in a pair of one-dimensional complex Ginzburg-Landau (CGL) systems, diffusive connections can induce amplitude death. Stability analysis of a spatially uniform steady state in coupled CGL systems reveals that amplitude death never occurs in a pair of identical CGL systems coupled by no-delay connection, but can occur in the case of delay connection. Moreover, amplitude death never occurs in coupled identical CGL systems with zero nominal frequency. Based on these analytical results, we propose a procedure for designing the connection delay time and the coupling strength to induce spatial-robust stabilization, that is, a stabilization of the steady state for any system size and any boundary condition. Numerical simulations are performed to confirm the analytical results.
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Affiliation(s)
- Hakui Teki
- Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 Japan
| | - Keiji Konishi
- Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 Japan
| | - Naoyuki Hara
- Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 Japan
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Zou W, Sebek M, Kiss IZ, Kurths J. Revival of oscillations from deaths in diffusively coupled nonlinear systems: Theory and experiment. CHAOS (WOODBURY, N.Y.) 2017; 27:061101. [PMID: 28679221 DOI: 10.1063/1.4984927] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching phenomena in coupled nonlinear systems. As a reverse issue of AD and OD, revival of oscillations from deaths attracts an increasing attention recently. In this paper, we clearly disclose that a time delay in the self-feedback component of the coupling destabilizes not only AD but also OD, and even the AD to OD transition in paradigmatic models of coupled Stuart-Landau oscillators under diverse death configurations. Using a rigorous analysis, the effectiveness of this self-feedback delay in revoking AD is theoretically proved to be valid in an arbitrary network of coupled Stuart-Landau oscillators with generally distributed propagation delays. Moreover, the role of self-feedback delay in reviving oscillations from AD is experimentally verified in two delay-coupled electrochemical reactions.
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Affiliation(s)
- Wei Zou
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam D-14415, Germany
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