Complex dynamics in a class of nearly-symmetric competitive CNNs

The paper analyzes bifurcations and complex dynamics in a class of nearly symmetric standard cellular neural networks (CNN). A one-parameter family of fourth-order CNN is introduced, which exhibits a cascade of period-doubling bifurcations leading to the birth of a complex attractor, close to some nominal symmetric CNN. The novelty with respect to previous work on this topic, is that the bifurcations and complex dynamics are obtained for small relative errors with respect to the nominal interconnections. The dynamical properties of the introduced class of fourth-order CNN, which are characterized by negative (inhibitory) interconnections between distinct neurons, are explained on the basis of a technique proposed by Smale (1976) to embed a given dynamical system within a competitive dynamical system of larger order.