Chaos control on universal learning networks

A new chaos control method is proposed which is useful for taking advantage of chaos and avoiding it. The proposed method is based on the following facts: (1) chaotic phenomena can be generated and eliminated by controlling the maximum Lyapunov exponent of the systems, and (2) the maximum Lyapunov exponent can be formulated and calculated by using higher-order derivatives of universal learning networks (ULNs). ULNs consist of a number of interconnected nodes which may have any continuously differentiable nonlinear functions in them and where each pair of nodes can be connected by multiple branches with arbitrary time delays. A generalized learning algorithm has been derived for the ULNs in which both first-order derivatives (gradients) and higher-order derivatives are incorporated. In simulations, parameters of ULNs with bounded node outputs were adjusted for the maximum Lyapunov exponent to approach the target value, and it has been shown that a fully-connected ULN with three sigmoidal function nodes is able to generate and eliminate chaotic behaviors by adjusting these parameters.