Numerical simulation and Hopf bifurcation solutions of flux neuron system with double time delays

Abstract

In this paper, a double time-delay flux neuron system with magnetron memristor is proposed by the classical HR neuron system. The stability, existence, direction of bifurcation and bifurcation cycle solution of the system are studied by using Routh Hurwitz judgment method and central manifold theorem in our work [18]. we mainly study Numerical simulation solution on the time series diagram and phase diagram of the system under different time lag by numerical simulation with MATLAB software. The simulation shows that under appropriate conditions, the time delay is less than a critical value, and the system is asymptotically stable. When the time delay exceeds the critical value, Hopf bifurcation occurs at the equilibrium point of the system. As a result, through the numerical simulation diagram, we intuitively obtain that there exists a bifurcation periodic solution in the specific time-delay range of the system, and the change law of spike discharge behavior induced by increasing double time-delay is clarified, which is helpful to explain the abnormal discharge behavior of brain or nerve center caused by electromagnetic radiation.