Enhancing chaos in chaotic maps and flows

Abstract

We propose a mechanism by which the degree of chaoticity as measured by the average Lyapunov exponent in chaotic flows can be increased. Our mechanism consists of introducing small changes in the system parameters in regions of phase space where the local Lyapunov exponent falls substantially below its average value. We have applied our mechanism to several typical chaotic flows and maps, dissipative as well as area preserving. An interesting consequence of this increase in chaoticity is an enhancement of the rate of mixing of the system. We find that our method is quite efficient as it gives a substantial enhancement of chaos as measured by the average Lyapunov exponent and also the rate of mixing for small changes in system parameters.