Study On Chaoticity Of Memristive Neural Network And Synchronization Control Of Several Delayed Neural Networks

Artificial neural network with a high degree of parallelism, nonlinear effects, good fault tolerance and associative memory function and adaptive, self-learning function, it has been widely used in engineering technology. Due to the finite switching speed of amplifiers and communication, time delays exist in neural networks, which lead to very complex dynamical behaviors such as oscillations, bifurcation, and chaos, etc. Hence, many researchers have focused on the delayed neural networks. In this dissertation, we studied the chaoticity of memristive neural network and synchronization control of several delayed neural networks. The main works are as follows:1. The memristive neural network is studied. By computer programming meth-ods, the topology Horseshoe of memristor neural network is found, which confirmed the chaotic behavior of the memristive Hopfield neural network.2. The memristive delayed competitive neural network is investigated. By construct-ing a proper Lyapunov-Krasovskii functional, as well as employing differential inclusions theory, a feedback controller is designed to achieve the asymptotic synchronization of coupled competitive neural networks.3. The synchronization of stochastic delayed competitive neural networks with dif-ferent timescales and reaction-diffusion terms is considered. By employing the LaShall-type invariance principle for stochastic differential delay equations, and the linear matrix inequality (LMI) technique, a feedback controller is designed to achieve the asymptotical synchronization of coupled stochastic competitive neural networks.4. The delayed Cohen-Grossberg neural network is studied. By using the Lyapunov-Krasovskii functional, stochastic analysis technology, a sufficient condition on the asymp-totic stability for the considered system is obtained. The condition not only connects with the delays and diffusion effect, but also relates to the magnitude of noise. Then, by using Lyapunov stability theory and Barbalat’s lemma, an adaptive feedback controller is presented to achieve the synchronization of different Cohen-Grossberg chaotic neural networks with unknown parameters.5. The projective synchronization of nonidentical chaotic neural networks with mixed time delays is investigated. By considering a proper sliding surface and construct- ing Lyapunov-Krasovskii functional, as well as using the linear matrix inequality (LMI) technique, a sliding mode controller is designed to achieve the projective synchronization of the different neural networks.