Generalized Stability in an Array of Nonlinear Dynamic Systems with Applications to Chaotic CNN

This paper introduces a generalized stability with respect to a transformation (GST) for a coupled discrete array of difference systems (CDADS) and a coupled continuous array of differential systems (CCADS). Some constructive theorems provide general representations of GST in both CDADS and CCADS. Using these theorems, one can design GST-based CADS and CCADS via appropriate transformations. As examples, the results are applied to autonomous and nonautonomous coupled discrete and differentiable Lorenz cellular neural network (CNN) CADS and CCADS; differentiable Chen CNN CCADS, and discrete sine-function CNN CADS. Extensive numerical simulations show their complex dynamic behaviors. The established theorems provide insights for better understanding of some new phenomena of complex discrete and continuously-differentiable networks.