Bifurcation Analysis On A Neural Network Model With Delays

A simplified neural network model with three neurons and three delays is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the distribution of roots of the associated characteristic equation, its linear stability of the zero equilibrium is investigated. Then, choose one of the delays as a bifurcation parameter. We assume that the system undergoes a Hopf bifurcation at the zero equilibrium when the bifurcation parameter passes through a critical value. In the sequel, using the normal form theory and center manifold reduction due to Hassard et al., we are able to determine the Hopf bifurcation direction and the properties of the bifurcation periodic solutions, for example, stability on the center manifold and period.The first part introduces the development and analyzing methods of bifurcation. The second part is about introduction of the basic conception and analyzing methods of bifurcation, include Floquent theory, normal form theory, center manifold theory and Hopf theory. The third part is my own work in which a simplified neural network model with three neurons and three delays is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. The last part is the summery of the whole paper...