Hybrid control on stability and bifurcation for a single neuron network affected by distributed and leakage delay

In this paper, a neuron system with leakage and distributed delay is considered. This paper investigates classical dynamical problems such as local stability and Hopf bifurcation. Then, the Hopf bifurcation of the single neuron network is controlled by designed controller. By using the leakage delay as the bifurcation parameter and analyzing the associated characteristic equation, we find that when the bifurcation parameter passes through some critical value, the system come into being a Hopf bifurcation. Besides, by changing parameter of the feedback gain, the position of the bifurcation point can be changed by the controller and desirable dynamics can be achieved. Finally, numerical simulations are given to substantiate the theoretical analysis.