Effects of time delays on dynamics of flux e-HR neuron model

Abstract

Since time delays are very vital and inevitable in the transmission of neurons, this paper is mainly concerned with the dynamic analysis of the magnetic flux e-HR neuron model with time delays. Specifically, the stability of the system at the equilibrium point and the conditions for bifurcations are analyzed to explore the impact of time delays on dynamics behavior. Results show that the system exhibits Hopf bifurcation within the specific range of time delay. Moreover, the increase of time delay can induce the tip discharge behavior. In addition, we investigate the stability and bifurcation behavior of the model with dual time delays. Our results indicate that the system displays rich dynamics performance under certain conditions. Furthermore, numerical simulations show time delays play a crucial role in the dynamics process for the magnetic flux e-HR neuron model.