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Zbl 1069.34056
Ge, Zheng-Ming; Chen, Chien-Cheng
Phase synchronization of coupled chaotic multiple time scales systems. (English)
[J] Chaos Solitons Fractals 20, No. 3, 639-647 (2004). ISSN 0960-0779

The authors study phase synchronization of two coupled chaotic oscillators. Two oscillators are said to be phase synchronized if one can introduce their phases $\varphi_1(t)$ and $\varphi_2(t)$ and the phases satisfy the locking condition $\vert n \varphi_1(t) - m \varphi_2(t)\vert < \text{ const}$, where $n$ and $m$ are some integer numbers. \par Using numerical simulations of the Hindmarsh-Rose neuron model and of a model for the brushless dc rotor, the authors conclude that the behavior of Lyapunov exponents can not be used as a criterion for the phase synchronization of coupled systems. The given arguments are purely numerical.
[Sergiy Yanchuk (Berlin)]

MSC 2000:: *34C15 Nonlinear oscillations of solutions of ODE
34C28 Other types of "recurrent" solutions of ODE
34D08 Lyapunov exponents

Keywords: phase synchronization; coupled systems; multiple scales; Lyapunov exponents

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