Stability And Hopf Bifurcation Of A BAM Neural Network

The dynamics of neural network,which has been applied widely,is the foundation of application and design.Considering that there is time-lag in the transference of information between neurons in the neural network,the neural network models described by difference equations and differential equations should contain delyas. Due to the shortage of efficient tool and method in the qualitative anaylsis of large delayed difference and differential equations,while the dynamical study of small delayed neural network models can provide useful method and tool to investigation of large network,so it is meaningful that we study the dynamics of small difference equations and differential equations neural networks with delays.This thesis is built on the basis above.The focus of this thesis is to study issues related to stability and bifurcation of a BAM neural network with delayed self-feedback and a BAM neural network with delays.Firstly,we give the formulation of the model.Secondly,we analyze the stability of the synchronized model by using eigenvalue method.We study the stability of the model by linearizing locally the nonlinear system at the equilibrium. Then,by means of the standard Hopf bifurcation theory,we obtain a branch of periodic solutions.Based on the normal form approach and the center manifold theory,we derive the formula determining the properties of Hopf bifurcating periodic orbit for a bidirectional associative memory of neurons with delays,such as the direction of Hopf bifurcation,stability of the Hopf bifurcating periodic orbits and so on.Finally,numerical simulations are given with two examples to illustrate the previous results.