A new chaotic Hopfield neural network and its synthesis via parameter switchings

In this paper, we present a new chaotic attractor in Hopfield neural network. Numerical experiments show that the presented Hopfield neural network can display complex dynamics by changing the self-connection weight. Surprisingly, coexistence of a chaotic attractor and a limit cycle is found in this system, which means, the system can exhibit a chaotic attractor or a limit cycle according to different initial values, and this phenomenon is never reported before. We give a rigorous verification of existence of horseshoe chaos by virtue of topological horseshoes theory and estimates of topological entropy in the derived Poincaré maps. Finally, synthesis of the chaotic attractor is studied via parameter switching and a numerical example illustrates the effectiveness of this method.