Inferring Global Synchrony from Local Symbolic Dynamics

نویسندگان

  • Sarika Jalan
  • Fatihcan M. Atay
  • Jürgen Jost
چکیده

We present a method based on symbolic dynamics for the detection of synchronization in networks of coupled oscillators. The symbolic dynamics are defined using special partitions of the phase space which prevent the occurrence of certain symbol sequences related to the characteristics of the dynamics. These partitions are chosen to best distinguish chaotic (but deterministic) dynamics from random ones in the uncoupled case. In the coupled case, they allow for a rapid detection of qualitative types of emerging collective dynamics. As a direct application, we can detect synchronization of coupled chaotic dynamics on networks from a single randomly selected node by comparing the transition probabilities with those of the uncoupled function. The method utilizes a relatively short time series of measurements and hence is computationally very fast. Furthermore, it is robust against parameter uncertainties, is independent of the network size, and does not require knowledge of the connection structure. We present our method for the one-dimensional logistic map, the two-dimensional Hénon map, and the three-dimensional Lorenz oscillator as local dynamical function, and for various different coupling structures.

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تاریخ انتشار 2006