Detectability of non-differentiable generalized synchrony

Details Detectability of non-differentiable generalized synchrony Detectability of non-differentiable generalized synchrony

2003-03-11

arxiv.org/abs/nlin/0303022v1

Nonlinear Sciences

Chaotic Dynamics

8 pages, 8 figures, submitted to PRE

Scientific paper

10.1103/PhysRevE.67.066218

Generalized synchronization of chaos is a type of cooperative behavior in directionally-coupled oscillators that is characterized by existence of stable and persistent functional dependence of response trajectories from the chaotic trajectory of driving oscillator. In many practical cases this function is non-differentiable and has a very complex shape. The generalized synchrony in such cases seems to be undetectable, and only the cases, in which a differentiable synchronization function exists, are considered to make sense in practice. We show that this viewpoint is not always correct and the non-differentiable generalized synchrony can be revealed in many practical cases. Conditions for detection of generalized synchrony are derived analytically, and illustrated numerically with a simple example of non-differentiable generalized synchronization.

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