Chaos criteria and chaotification schemes on a class of first-order partial difference equations.

Abstract

This article is involved in chaos criteria and chaotification schemes on one kind of first-order partial difference equations having non-periodic boundary conditions. Firstly, four chaos criteria are achieved by constructing heteroclinic cycles connecting repellers or snap-back repellers. Secondly, three chaotification schemes are obtained by using these two kinds of repellers. For illustrating the usefulness of these theoretical results, four simulation examples are presented.