Synchronization Control And Multiple Stability Analysis Of Neural Dynamical System

Neurodynamic system as a very special dynamic system,has a wide of applications in mathematics,engineering,physics,and biology and so on.In recent years,the neurodynamic system has become a hot research theme.The application of the neurodynamic system is strongly dependent on the dynamic characteristics of the system.Therefore,it is of great theoretical and practical significance to study the dynamic characteristics of neurodynamic system.This paper mainly explores the three types of neurodynamic systems.By employing Laplace transforms,differential equation theory,fixed point theory of Brouwer,inequality techniques,Lyapunov functional methods,Green formula,Ito formula,and combining the concrete structure of the neurodynamic system,the criterion of judgment of the neuraodynamic system is obtained.The main work of this thesis is summarized as follows:Firstly,the stochastic synchronization problem of a linear coupled neurodynamic system with directed topology and reaction diffusion term is investigated.As we all know,due to the complexity of system structure,the emergence of spatial variables and the change of time are difficult for synchronous implementation of neurodynamic system.By employing local information of random network nodes,for two neurodynamic systems with special structure,that is,directed spanning tree and directed generation path,we get the criterion of synchronization.Secondly,the problem of the synchronization of the fractional-order coupling neurodynamic system with reaction-diffusion term is investigated.A class of fractional-order nurodynamic systems with reaction diffusion term is established.By using related knowledge of fractional-order differential equations,the dynamics behavior of neurodynamic system is investigated.The synchronization of the integer-order coupled neural network with reaction diffusion term is extended to the synchronization of fractional-order coupled neural networks,which provides new ideas for analyzing the synchronization of fractional-order coupled neural networks with reaction-diffusion terms.Thirdly,multiple Mittag-Leffler stability of fractional-order Cohen-Grossberg neurodynamic system with non-monotonic piecewise linear activation functions is analyzed.Based on the related knowledge of fractional-order differential equations and non-monotone analysis knowledge,the multiple Mittag-Leffler stability is analyzed and the existing related results are extented.To sum up,in this thesis,three kinds of neurodynamic systems are investigated,especially for neurodynamic system with reaction-diffusion terms,which lays a foundation for further analysis of systems with reaction-diffusion terms.