Rapid fluctuation for topological dynamical systems

Abstract

In this paper, we introduce a new notion called rapid fluctuation to characterize the complexity of a general topological dynamical system. As a continuation of the former work [Huang, Chen, Ma, J. Math. Anal. Appl., 2006, 323: 228–252], here we prove that a Lipschitz dynamical system defined on a compact metric space has a rapid fluctuation if it has either a quasi shift invariant set or a topological horseshoe. As an application, the rapid fluctuation of a discrete predator-prey model is considered.