Complicated dynamics of a ring neural network with time delays
Xu Xu · Journal of Physics A Mathematical and Theoretical · 2008
This paper studies the dynamical behavior of a ring neural network with time delays. On the basis of Lyapunov's method, the asymptotic stability of the equilibrium is first investigated, and the delay-dependent criteria ensuring global stability for the ring neural network are obtained. Moreover, based on the global Hopf bifurcation theorem for FDE, the conditions that guarantee the global existence of periodic solutions are determined. It shows that periodic solutions bifurcating from the trivial equilibrium can continue when the time delay is far away from the critical value. Some examples are induced to illustrate our results. In addition, complicated dynamics of the model are investigated with the help of numerical simulation. The study results show that the model exhibits period-doubling bifurcations which lead eventually to chaos; and the chaos can also directly occur via the bifurcations from the quasi-periodic solutions.