Chaotic Dynamics of a Two-Dimensional Spatiotemporal Discrete System with Delayed Perturbations

This paper is mainly concerned with the existence of chaos in a two-dimensional spatiotemporal discrete system with delayed perturbations. By applying the snap-back repeller theory, two criteria of chaos in the sense of both Li-Yorke and Devaney are established. Moreover, the lower bounds of the parameters that make the system chaotic are obtained. Finally, an example and its computer simulations of the dynamical behavior, spatiotemporal graphs, and the trends of the largest Lyapunov exponents with respect to the initial values and parameters are given to demonstrate the correctness of the theoretical results.