Driving systems with chaotic signals

Abstract

Negativity of the conditional Lyapunov exponents is a necessary and in many cases a sufficient condition for the occurrence of synchronization between a chaotic drive and the response subsystem. Treating one of the variables of coupled logistic maps as the drive, our numerical simulations show that the negativity of the conditional Lyapunov exponents does not always guarantee synchronization and, additionally, the domain of initial conditions for the drive variables needs to be specified in which case the synchronization occurs. Additionally, an example showing the pitfalls of the numerical study of synchronization when the conditional Lyapunov exponent is positive is presented.