The Stability And Global Hopf Bifurcation Of Classes Of Delay Differential Systems

This thesis is concerned with the stability and global Hopf bifurcation of delay differential systems. There are a number of retarded differential equations in physics, ecology, epidemiology, social-ecology and many other fields. So that it is important to realize the dynamical behaviors of these models. Bifurcation theory is an important problem in differential systems with delay.First, The theories of Local bifurcation and global bifurcation were given, which are the base of this paper.Second, A second order delayed predator-prey systems was discussed. The conditions of the existence of equilibria and local Hopf bifurcation were given, further, we study the existence of global Hopf bifurcation.At last, We studied the stability and ioacal Hopf bifurcation for A three-order lac operon regulatory networks model. Combing the global Hopf bifurcation for general functional differential equations, We investigate the existence of global Hopf bifurcation.