Abstract
In this review article we discuss effects of phase synchronization of nonlinear self-sustained oscillators. Starting with a classical theory of phase locking, we extend the notion of phase to autonoumous continuous-time chaotic systems. Using as examples the well-known Lorenz and R o ssler oscillators, we describe the phase synchronization of chaotic oscillators by periodic external force. Both statistical and topological aspects of this phenomenon are discussed. Then we proceed to more complex cases and discuss phase synchronization in coupled systems, lattices, large globally coupled ensembles, and of space-time chaos. Finally, we demonstrate how the synchronization effects can be detected from observations of real data.
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