Discrete-continuous control of bifurcations and oscillatory behaviour in a class of Cellular Neural Networks

In this paper we study a class of third order Cellular Neural Networks (CNNs) with competitive interconnections between distinct neurons. Existence of bifurcations and oscillations is proved for such network. Over the past few decades, one of the most exciting and interesting ideas developed in nonlinear dynamics is that concerning the complex and chaotic behavior of the systems. Recently, novel applications where the chaos has to be controlled have been studied. In this direction we design a discrete-continuous regulator of such class of CNNs in order to stabilize the chaotic motion to an admissible solution which is connected in some way to the original behavior of the system. The control aim is to remove the chaotic behavior without modifying the essential features of the given system far from this behavior. Numerical simulations verify the obtained theoretical results.