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.

• Received 11 December 2001

DOI:https://doi.org/10.1103/PhysRevE.65.046215