Transient chaos measurements using finite-time Lyapunov exponents

Abstract

The notion of finite-time Lyapunov exponent averaged over initial conditions is used for characterizing transient chaos observed in one-dimensional maps. A model of its dependence on time is verified by comparing theoretically predicted values with those obtained numerically. Finally, the same model is used for estimating duration of transient chaos (rambling time) for some maps from the logistic family. © 2010 American Institute of Physics.