Chaotification for a Class of First-Order Partial Difference Equations

This paper is concerned with chaotification for a class of first-order partial difference equations, in which the system size is finite or infinite. Nine new chaotification schemes for the class of first-order partial difference equations with general controllers, mod-operation, and sawtooth functions are established, respectively. All the controlled systems are proved to be chaotic in the sense of both Devaney and Li–Yorke. In addition, five new chaotification schemes for general discrete dynamical systems in finite-dimensional real spaces and l ∞ are established. Two illustrative examples are provided with computer simulations.