Chaotification of First-Order Partial Difference Equations

This paper is concerned with chaotification of first-order partial difference equations. Two criteria of chaos for the difference equations with general controllers are established, and all the controlled systems are proved to be chaotic in the sense of Li-Yorke or of both Li-Yorke and Devaney by applying the coupled-expanding theory of general discrete dynamical systems. The controllers used in this paper can be easily constructed, facilitating the chaotification of first-order partial difference equations. For illustration, two illustrative examples are provided.