Stability and Hopf bifurcation solutions of flux neuron model with double time delays

In this paper, based on the classical HR neuron model, a double time-delay flux neuron model with magnetron memristor is proposed in this paper. The stability, the existence of Hopf bifurcation, direction of bifurcation and bifurcation cycle solution of the model are studied using Routh Hurwitz judgment method and central manifold theorem. As a result, we prove that there exists a bifurcation periodic solution in the specific time-delay range of the model, 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. The time-series diagram and phase diagram of the model under different time lag are obtained by numerical simulation with MATLAB software. The simulation result 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