Fourth-Order Nearly-Symmetric CNNS Exhibiting Complex Dynamics

In this paper, the possible presence of complex dynamics in nearly-symmetric standard Cellular Neural Networks (CNNs), is investigated. A one-parameter family of fourth-order CNNs is presented, which exhibits a cascade of period-doubling bifurcations leading to the birth of a complex attractor, close to some nominal symmetric CNN. Different from previous work on this topic, the bifurcations and complex dynamics are obtained for small relative errors with respect to the nominal interconnections. The fourth-order CNNs have negative (inhibitory) interconnections between distinct neurons, and are designed by a variant of a technique proposed by Smale to embed a given dynamical system within a competitive dynamical system of larger order.