Chaotification of a class of discrete systems based on heteroclinic cycles connecting repellers in Banach spaces

This paper is concerned with chaotification of a class of discrete dynamical systems in Banach spaces via the feedback control technique. A chaotification theorem based on heteroclinic cycles connecting repellers for maps in Banach spaces is established. The controlled system is proved to be chaotic in the sense of both Devaney and Li–Yorke. An illustrative example is provided with computer simulations.