Detectability of nondifferentiable generalized synchrony.

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 nondifferentiable 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 nondifferentiable 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 nondifferentiable generalized synchronization.