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Onset of colored-noise-induced synchronization in chaotic systems

Yan Wang1,2, Ying-Cheng Lai1,3, and Zhigang Zheng2

  • 1Department of Electrical Engineering, Arizona State University, Tempe, Arizona 85287, USA
  • 2Department of Physics, Beijing Normal University, Beijing 100875, China
  • 3Department of Physics, Arizona State University, Tempe, Arizona 85287, USA

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Phys. Rev. E 79, 056210 – Published 12 May, 2009

DOI: https://doi.org/10.1103/PhysRevE.79.056210

Abstract

We develop and validate an algorithm for integrating stochastic differential equations under green noise. Utilizing it and the standard methods for computing dynamical systems under red and white noise, we address the problem of synchronization among chaotic oscillators in the presence of common colored noise. We find that colored noise can induce synchronization, but the onset of synchronization, as characterized by the value of the critical noise amplitude above which synchronization occurs, can be different for noise of different colors. A formula relating the critical noise amplitudes among red, green, and white noise is uncovered, which holds for both complete and phase synchronization. The formula suggests practical strategies for controlling the degree of synchronization by noise, e.g., utilizing noise filters to suppress synchronization.

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Phys. Rev. E 79, 056210– Published 12 May, 2009
  • Received 11 December 2008

© 2009 American Physical Society

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