Dynamic Analysis Of Several Kinds Of Delayed Neural Networks

Delayed neural networks have been widely used in signal processing,remote sensing,quantum neural equipment and systems,which have attracted the attention of scholars and researchers all over the world.The successful implementation of these practical applications depends heavily on the dynamics of the designed neural networks.Therefore,it is of great importance to investigate the nonlinear dynamics of delayed neural networks including stability,bifurcation,synchronization,oscillation and chaos.The thesis investigates the dynamical properties of several kinds of delayed neural networks and the adaptive synchronization of fractional-order complex-valued neural networks with time delay,and the theoretical analysis and the results are proved by Matlab simulation.It consists of five chapters,as follows:In chapter one,the paper mainly introduces relevant knowledge and theorems about delayed neural networks,including fractional calculus theory,adaptive control theory,central manifold theorem and normal form theory,etc.,and expounds the main contents of this paper.In chapter two,the stability and bifurcation of a three-neuron network with multiple discrete and distributed delays are studied.Firstly,by investigating the eigenvalue distribution of the corresponding characteristic equations of the linearized system,the critical conditions for the stability and bifurcation of the system are obtained.Secondly,the bifurcation direction and the stability condition of the bifurcation periodic solution are studied by using the normal form theory and the center manifold theorem.In chapter three,the stability and bifurcation of complex-valued neural networks with multiple discrete and distributed delays are studied.First,it is a separation variable.By assuming that the activation function can be separated into real part and the imaginary part,the critical condition of the asymptotic stability and bifurcation of the neural network is obtained.Secondly,the bifurcation direction and the stability condition of the bifurcation periodic solution are studied by using the normal form theory and the center manifold theorem.In chapter four,the adaptive synchronization of fractional-order complex-valued neural networks with discrete and distributed delays is studied.Based on the adaptive control method and the Lyapunov function theory,a controller is designed and the sufficient conditions for realizing the synchronization of a fractional complex time delay neural network are given.In chapter five,we summarize the main work of this paper and discuss the content and results.In addition,some future research directions are prospected.