Bifurcation analysis and Hamiltonian energy control of mHR Neuron model

It is very important to study the effect of external energy on the firing of neurons for controlling the information encoding and transmission in the nervous system. In this paper, the bifurcation behavior of mHR Neuron model in two parameter plane and the control of its discharge pattern are studied by using the method of Helmholtz theorem and numerical simulation. The numerical simulation shows that the mHR neural model has abundant bifurcation phenomenon, such as period-doubling bifurcation, period-doubling bifurcation and period-adding bifurcation in different parameter planes. On this foundation, in order to control the chaotic discharge pattern of the Neuron model, the Hamiltonian energy feedback controller is applied to the neuron system. It is found that by adjusting the parameters of the controller, the firing pattern of neurons can be controlled effectively. It is of practical significance to understand the energy consumption and stability of complex neuron system.