Synchronization Analysis Of Several Classes Of Neural Networks

Based on differential inclusions, non-smooth analysis, Lyapunov method, and linearmatrix inequality(LMI), by design appropriate controllers, this dissertation studies globalexponential synchronization of Cohen–Grossberg neural networks with discontinuousneuron activation, synchronization of reaction-diffusion neural networks with mixed timedelays, and synchronization control of chaotic memristive neural networks. The maincontent of the dissertation is listed as follows:(1). The exponential synchronization issue of delayed Cohen-Grossberg neuralnetworks with discontinuous activations has been investigated. By utilizing Lyapunovstability theory, an adaptive controller is designed such that the response system can beexponentially synchronized with a drive system. The synchronization criteria are easilyverified and the obtained results are also applicable to neural networks with continuousactivations since they are a special case of neural networks with discontinuousactivations.(2). The synchronization issue for reaction-diffusion neural networks with mixedtime-varying delays has been studied. State feedback and adaptive controllers aredesigned respectively such that the response system can be synchronized withcorresponding drive system. In addition, when the external disturbances appear in thenetworks, an adaptive controller is designed to guarantee the H synchronization forthe networks.(3). This section treats of the exponential synchronization issue of memristivedelayed neural networks. And here, we adopt non-smooth analysis and control theory tohandle memristor-based chaotic neural networks with discontinuous right-hand side. Byapplying Lyapunov-Krasovskii functional stability theory and approach, several newcriteria guaranteeing exponential synchronization of the drive-response memristor-basedchaotic neural networks are obtained via discontinuous impulsive control.