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Brownian Behavior in Coupled Chaotic Oscillators

Author

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  • Francisco Javier Martín-Pasquín

    (Centro de Tecnología Biomédica, Universidad Politécnica de Madrid, 28040 Madrid, Spain)

  • Alexander N. Pisarchik

    (Centro de Tecnología Biomédica, Universidad Politécnica de Madrid, 28040 Madrid, Spain
    Neuroscience and Cognitive Technology Laboratory, Innopolis University, 420500 Kazan, Russia)

Abstract

Since the dynamical behavior of chaotic and stochastic systems is very similar, it is sometimes difficult to determine the nature of the movement. One of the best-studied stochastic processes is Brownian motion, a random walk that accurately describes many phenomena that occur in nature, including quantum mechanics. In this paper, we propose an approach that allows us to analyze chaotic dynamics using the Langevin equation describing dynamics of the phase difference between identical coupled chaotic oscillators. The time evolution of this phase difference can be explained by the biased Brownian motion, which is accepted in quantum mechanics for modeling thermal phenomena. Using a deterministic model based on chaotic Rössler oscillators, we are able to reproduce a similar time evolution for the phase difference. We show how the phenomenon of intermittent phase synchronization can be explained in terms of both stochastic and deterministic models. In addition, the existence of phase multistability in the phase synchronization regime is demonstrated.

Suggested Citation

  • Francisco Javier Martín-Pasquín & Alexander N. Pisarchik, 2021. "Brownian Behavior in Coupled Chaotic Oscillators," Mathematics, MDPI, vol. 9(19), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2503-:d:650723
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    References listed on IDEAS

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    1. P. Gaspard & M. E. Briggs & M. K. Francis & J. V. Sengers & R. W. Gammon & J. R. Dorfman & R. V. Calabrese, 1998. "Experimental evidence for microscopic chaos," Nature, Nature, vol. 394(6696), pages 865-868, August.
    2. Alves, Samuel B. & de Oliveira, Gilson F. & de Oliveira, Luimar C. & Passerat de Silans, Thierry & Chevrollier, Martine & Oriá, Marcos & de S. Cavalcante, Hugo L.D., 2016. "Characterization of diffusion processes: Normal and anomalous regimes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 392-401.
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    1. Saša Nježić & Jasna Radulović & Fatima Živić & Ana Mirić & Živana Jovanović Pešić & Mina Vasković Jovanović & Nenad Grujović, 2022. "Chaotic Model of Brownian Motion in Relation to Drug Delivery Systems Using Ferromagnetic Particles," Mathematics, MDPI, vol. 10(24), pages 1-19, December.

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