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 fa cts: 1) chaotic phenomena can be generated and eliminated by controlling ma ximum Lyapunov exponent of systems and 2) maximum Lyapunov exponent can be formulated and calculated by using higher order derivatives of Universal Le arning Networks (ULN's). ULN's consist of a number of inter-connected nodes where the nodes may have any continuously differentiable nonlinear functio ns in them and each pair of nodes can be connected by multiple branches wit h arbitrary time delays. A, generalized learning algorithm has been derived for the ULN's, in which both the first-order derivatives (gradients) and t he higher order derivatives are incorporated. In simulations, parameters of ULN's with bounded node outputs are adjusted for maximum Lyapunov componen t to approach the target value. And, it has been shown that a fully connect ed ULN with three sigmoidal function nodes is able to generate and eliminat e chaotic behaviors by adjusting the parameters.