Estimation of the dominant Lyapunov exponent of non-smooth systems on the basis of maps synchronization

A novel method of estimation of the largest Lyapunov exponent for discrete maps is introduced and evaluated for chosen examples of maps described by difference equations or generated from non-smooth dynamical systems. The method exploits the phenomenon of full synchronization of two identical discrete maps when one of them is disturbed. The presented results show that this method can be successfully applied both for discrete dynamical systems described by known difference equations and for discrete maps reconstructed from actual time series. Applications of the method for mechanical systems with discontinuities and examples of classical maps are presented. The comparison between the results obtained by means of the known algorithms and novel method is discussed.