Stability And Hopf Bifurcation In A Delayed System Of Neural Netwoks

In this thesis, the stability and Hopf bifurcation of a neural network model described by a delay differential equation are investigated.The stability analysis of the trivial equilibrium is carried out on the basis of stability switches, a phenomenon that the equilibrium may change its stability as a control parameter varies. Analysis with numerical simulation shows that the equilibrium may not change its stability at all or changes its stability up to a finite number of times. At the critical values of the control parameter where the system admits a stability switch, a Hopf bifurcation occurs.The local dynamics of a Hopf bifurcation analysis is studied by using the pseudo-oscillator analysis, and the bifurcation direction, stability and the amplitude the periodic solution near the Hopf bifurcation are determined. Compared with the current methods such as the center manifold reduction together with Normal Form, the pseudo-oscillator analysis involves only easy computation, and gives pretty accurate prediction of the periodic solution resulted from the Hopf bifurcation, confirmed numerically by using XPPAUT.