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Synchronization induced by alternation of dynamics

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  • Rosas, Alexandre

Abstract

Synchronization in arrays of interacting units has received considerable attention in the past five decades as models of phenomena ranging over a broad set of temporal and spatial scales, from cellular biology to neural networks to the flocking of birds as some examples. Most of this work has involved continuous coupled units. More recently, interest has included synchronization phenomena in arrays of discrete units, especially two-state and three-state units. Here we focus on arrays of three-state units and present a different synchronization mechanism than those established before. The usual mechanism is a limit cycle that occurs for some interaction parameter regimes. Our mechanism involves quick toggling between two parameters in a standard three-state model. Neither parameter alone leads to a limit cycle, but quick toggling between the two yields a trajectory similar to that of a limit cycle. We discuss the conditions for this toggling originated synchronization to occur and show that it is stable under noisy perturbations of the toggling time and the coupling parameters.

Suggested Citation

  • Rosas, Alexandre, 2021. "Synchronization induced by alternation of dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008158
    DOI: 10.1016/j.chaos.2021.111461
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    References listed on IDEAS

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    1. Ejlali, Nasim & Pezeshk, Hamid & Chaubey, Yogendra P. & Sadeghi, Mehdi & Ebrahimi, Ali & Nowzari-Dalini, Abbas, 2020. "Parrondo’s paradox for games with three players and its potential application in combination therapy for type II diabetes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
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    3. Gregory P. Harmer & Derek Abbott, 1999. "Losing strategies can win by Parrondo's paradox," Nature, Nature, vol. 402(6764), pages 864-864, December.
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    Cited by:

    1. Parastesh, Fatemeh & Dayani, Zahra & Bahramian, Alireza & Jafari, Sajad & Chen, Guanrong, 2023. "Performance of synchronization in networks of chaotic systems under different PID coupling schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    2. Lai, Joel Weijia & Cheong, Kang Hao, 2023. "Boosting Brownian-inspired games with network synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Lai, Joel Weijia & Cheong, Kang Hao, 2022. "Risk-taking in social Parrondo’s games can lead to Simpson’s paradox," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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