Chaos in first-order partial difference equations

This paper is concerned with chaos in 2D first-order partial difference equations with finite or infinite system size. By reformulating them into certain ordinary difference equations, several criteria of chaos are established, where some are induced by chaos in the corresponding scalar ordinary difference equation, and the others are implied by nondegenerate and regular snap-back repellers and regular snap-back repellers, respectively. Two illustrative examples are discussed with computer simulations.