Dynamic Optimization of Neuron Systems with Leakage Delay and Distributed Delay via Hybrid Control

This paper proposes a neuron system with both leakage delay and distributed delay. Typical dynamics including the local stability and Hopf bifurcation analysis are investigated. Then, a hybrid controller is designed to control the Hopf bifurcation of the proposed system. By regarding the leakage delay as the bifurcation parameter and further probing into the associated characteristic equation, we find that the system can generate a Hopf bifurcation when the bifurcation parameter passes through some critical value. Besides, the controller is capable of altering the bifurcation point and achieving desirable dynamics by changing the feedback gain parameter. Finally, numerical simulations are illustrated to substantiate the theoretical analysis.