Periodic Solution for a Complex-valued Network Model with Discrete Delay

For a tridiagonal two-layer real six-neuron model, the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature. In the present paper, we extend this two-layer real six-neuron network model into a complex-valued delayed network model. Based on the mathematical analysis method, some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established under the assumption that the activation function can be separated into its real and imaginary parts. Our sufficient conditions obtained by the mathematical analysis method in this paper are simpler than those obtained by the Hopf bifurcation method. Computer simulation is provided to illustrate the correctness of the theoretical results.