Nonlinear waves, patterns and spatio-temporal chaos in cellular neural networks

Spatio-temporal pattern formation occurring in discretely coupled nonlinear dynamical systems has been studied numerically. In this paper, we review the possibilities of using arrays of discretely coupled nonlinear electronic circuits to study these systems. Spiral wave initiation and Turing pattern formation are some of the examples. Sidewall forcing of Turing patterns is shown to be capable of driving the system into a perfect spatial organization, namely, a rhombic pattern, where no defects occur. The dynamics of the two layers supporting Turing and Hopf modes, respectively, is analysed as a function of the coupling strength between them. The competition between these two modes is shown to increase with the diffusion between layers. As well, the coexistence of low- and high-dimensional spatio-temporal chaos is shown to occur in one-dimensional arrays.