Chaotic Dynamics in a Class of Delay Controlled Partial Difference Equations

This paper is mainly concerned with the existence of chaos in a class of controlled partial difference equations via delay controllers. Using the snap-back repeller theory, four criteria of chaos in the sense of both Devaney and Li-Yorke in this system are established when the equation and the controller satisfy several relatively weak conditions. Moreover, two examples with computer simulations of their dynamical behaviors and the trends of the largest Lyapunov exponents with the initial values and parameters are discussed to illustrate the correctness of the theoretical results.