摘要：In this paper, we rigorously prove the existence of chaos in a class of delay difference equations, which can be viewed as a discrete analogue of a one-dimensional delay differential equation by using the Euler discretization. We first transform this class of delay difference equations into a high-dimensional discrete dynamical system. Then we prove that the map of the system is chaotic in the sense of both Devaney and Li-Yorke under some conditions, by employing the snap-back repeller theory. Finally, we give some computer simulations to illustrate the theoretical result. MSC:34C28, 37D45, 74H65.
关键词：chaos ; delay difference equation ; snap-back repeller ; chaos in the sense of Devaney ; chaos in the sense of Li-Yorke
