Synchronization Of Chaotic Neural Networks Delays Sampling

Chaos as one of the academic hot in the nonlinear science field, not onlypromotes the understanding of objective world, but also has widespread using instoring of information, system identification, parameter optimization and so on.Chaotic synchronization is an important branch in the fields of chaos, opens anew field for the application of chaos, with the progress of study on chaoticsynchronization method, its application has rapidly expanded to securecommunication, control, biology, sociology, economics and complex networks.Because chaotic system exists complex dynamic characteristics, it makes theresearch work of chaos control and synchronization more challenging. Thisarticle investigates the problem of sampled-data synchronization for delayedchaotic neural networks:1. The problem of sampled-data synchronization for chaotic neuralnetworks with discrete and distributed time-varying delays is investigated.Based on the Lyapunov stability theory, this article introduces twodelay-dependent terms, and constructs an appropriate Lyapunov functional.Through utilizing the Jensen inequality and free-weighting matrix method, somedelay-dependent synchronization criteria are obtained. Finally, a numericalexample verifies the designed sampled-data synchronization criteria have lessconservative.2. The problem of sampled-data synchronization of chaotic neuralnetworks with time delay in the leakage term and parametric uncertainties isstudied. Using the input delay method and Extended Wirtinger inequality, thisarticle constructs a novel Lyapunov functional and obtains the synchronizationcriteria in terms of linear matrix inequality (LMI). Numerical simulation andcomparison show the effectiveness and less conservatism of the designedsynchronization criteria.3. Applied the decomposition approach of delay interval and augmentedLyapunov functional method to the problem of sampled-data synchronizationfor chaotic neural networks with time-varying delays. This article presents the synchronization criteria in terms of LMI and designs the sampled-datacontroller in the presence of a constant input delay. In the numerical simulationexample, compared with other results in the literature, the effectiveness and lessconservatism of the designed synchronization criteria is demonstrated..4. The problem of sampled-data synchronization for chaotic neuralnetworks with random time-varying delays is investigated. We will regard thediscrete time delay as random variable which satisfies with Bernoullidistribution. When constructing the Lyapunov functional, this paper not onlyconsiders the characteristics of neuronal function, but also makes full use of thesampling control system characteristics. By using the method of convexcombination, the synchronization criterion which is in terms of LMI and thedesigned method of sampled-data controller are obtained. Finally, a numericalsimulation example verifies the correctness and effectiveness of thesampled-data synchronization criterion.