A model in a coupled system of simple neural oscillators with delays

We consider a coupled system of simple neural oscillators. Using the symmetric functional differential equation theories of Wu [J. Wu, Symmetric functional differential equations and neural networks with memory, Transactions of the American Mathematical Society 350 (12) (1998) 4799-4838], we demonstrate the multiple Hopf bifurcations of the equilibrium at the origin. The existence of multiple branches of bifurcating periodic solution is obtained. Then some numerical simulations support our analysis results.