Multistability and bifurcation in a delayed neural network

In this paper, the dynamical behaviors including multistability and bifurcation of a delayed neural network system are investigated. It is shown that the system coexists sixteen stable states with their own domains of attraction. All stable states are determined by using a Lyapunov function. Interestingly, the system exhibits bistability and double cycles with only one equilibrium. The existence of the Hopf bifurcation is well studied. It is shown that the Hopf bifurcation occurs as the time delay reaches a certain value. Simulation experiments supported our theoretical results.