## Phase synchronization of coupled chaotic multiple time scales systems.(English)Zbl 1069.34056

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 $$| n \varphi_1(t) - m \varphi_2(t)| < \text{ const}$$, where $$n$$ and $$m$$ are some integer numbers.
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.

### MSC:

 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations 34D08 Characteristic and Lyapunov exponents of ordinary differential equations
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### References:

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