Synchronization of two Rössler Systems with Switching Coupling

Arturo Buscarino, Mattia Frasca, Luigi Fortuna
Dipartimento di Ingegneria Elettrica Elettronica e Informatica, Universita degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italy

Marco Branciforte
ST Microelectronics, Stradale Primosole 50, 95121 Catania, Italy

Julien Clinton Sprott
Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA

Received: 30 June 2016 / Accepted: 5 December 2016 / Published online: 20 December 2016


In this paper, we study a system of two Rössler oscillators coupled through a time-varying link, periodically switching between two values. We analyze the system behavior with respect to the switching frequency. By applying an averaging technique under the hypothesis of high switching frequency, we find that, although each value of the coupling is not suitable for synchronization, switching between the two at a high frequency makes synchronization possible. However, we also find windows of synchronization below the value predicted by this technique, and we develop a master stability function to explain the appearance of these windows. The spectral properties of the system provide a useful tool for understanding the dynamics and synchronization failure in some intervals of the switching frequency. An experimental setup based on a digital/analog circuit is also presented showing experimental results which are in good agreement with the numerical analysis presented.

Ref: A. Buscarino, M. Frasca, M. Branciforte, L. Fortuna, and J. C. Sprott, Nonlinear Dynamics 88, 673-683 (2017)

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