Synchronization and Simulation of Hyperchaotic Neural Networks with Time-delay
Jian Xu · Jisuanji fangzhen · 2010
The neural networks with time-delay are infinite-dimension nonlinear dynamic systems. They could exhibit hyperchaotic behaviors with multiple positive Lyapunov exponents. This class of systems can be well used in the field of secure communications because of their complex time-series. It deals with the asymptotic and exponential synchronization problems of a class of hyperchaotic neural networks with time-delay. Using the single-direction coupling concept, a nonlinear controller was designed to achieve the state synchronization of two identical hyperchaotic neural networks. Furthermore, based on the L-K method and Halanay inequality lemma, time-delay independent sufficient conditions on synchronization were derived. The complicated calculation of LMI was avoided and the controlling processes were simplified as the consideration of that controller gain matrixes were positive definite. The illustrative examples demonstrate the effectiveness of the synchronization scheme presented. The relationship of exponential synchronization rate and controlling parameters were given by the numerical calculation in the end.