Lyapunov exponents, noise-induced synchronization, and Parrondo's paradox.

We show that Lyapunov exponents of a stochastic system, when computed for a specific realization of the noise process, are related to conditional Lyapunov exponents in deterministic systems. We propose to use the term stochastically induced regularity instead of noise-induced synchronization and explain the reason why. The nature of stochastically induced regularity is discussed: in some instances, it is a dynamical analog of Parrondo's paradox.