Chapter 2 Phase synchronization: From periodic to chaotic and noisy

Publisher Summary The classical theory of synchronization distinguishes between forced synchronization by an external periodic driving force, and mutual synchronization between coupled oscillators. In both cases, manifestations of synchronization are the same. Synchronization of periodic self-sustained oscillators in the presence of noise shows that noise acts against synchronization in a sense that under the noise influence synchronization occurs only for a limited period. Synchronization includes a wide range of problems from different fields of nonlinear dynamics and statistical physics. The chapter concentrates on the synchronization of stochastic system, which exhibits the phenomenon of stochastic resonance and, therefore, possesses noise-controlled time scales. The chapter presents an illustrative example of how synchronization looks like in a periodically driven overdamped stochastic system. The classical case of synchronization of self-sustained oscillator is discussed and details of forced, mutual, and synchronization under noisy perturbation are presented in the chapter. The chapter provides several examples of synchronization in chaos and excitable media. Synchronization of stochastic systems by external signals and synchronization of stochastic resonance systems are discussed in the chapter.

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