Complex behavior of chaotic synchronization under dual coupling channels

Wenchao Yang, Zi-Gang Huang, Xingang Wang, Liang Huang, Lei Yang, Ying-Cheng Lai

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Abstract

Most previous works on complete synchronization of chaotic oscillators focused on the one-channel interaction scheme where the oscillators are coupled through only one variable or a symmetric set of variables. Using the standard framework of master-stability function (MSF), we investigate the emergence
of complex synchronization behaviors under all possible configurations of two-channel coupling, which include, for example, all possible cross coupling schemes among the dynamical variables. Utilizing the classic Rössler and Lorenz oscillators, we find a rich variety of synchronization phenomena
not present in any previously extensively studied, single-channel coupling configurations. For example, in many cases two coupling channels can enhance or even generate synchronization where
there is only weak or no synchronization under only one coupling channel, which has been verified in a coupled neuron system. There are also cases where the oscillators are originally synchronized under one coupling channel, but an additional synchronizable coupling channel can, however, destroy synchronization. Direct numerical simulations of actual synchronization dynamics verify the MSF-based predictions. Our extensive computation and heuristic analysis provide an atlas for synchronization of chaotic oscillators coupled through two channels, which can be used as a systematic reference to facilitate
further research in this area.
Original languageEnglish
Article number023055
Number of pages14
JournalNew Journal of Physics
Volume17
DOIs
Publication statusPublished - 18 Feb 2015

Keywords

  • synchronization
  • master stability function
  • dual channel coupling

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