Li-Yorke chaos in a class of controlled delay difference equations

Abstract

A class of controlled delay difference equations is considered. Proof of the existence of chaos in the sense of Li-Yorke in the controlled system is given by applying the snap-back repeller theorem. Conditions for the existence of chaos are weak and lots of functions can be taken as controllers, which facilitates the chaotification of delay difference equations. One illustrative example is provided with computer simulations.