Dynamic Response And Control Of A Kind Of Neuron Models

The biological nervous system is made up of many highly inline neurons,it's an essential part of the information transmission and processing.Neuroscience takes the neuron model as the research object and studies the firing activity of the nervous system.The study of the firing activity of the neuron model is essentially the reproduction of the electrophysiological activity in the cells of the nervous system.In real life,abnormal discharges of the neuronal system often lead to neurological diseases.Therefore,it has reference value to study the discharge activity of the nervous system and to control the stable discharge of the nervous system.In this paper,a kind of neuron model is taken as the research object,and the method combining simulation and theory is used to discussed the discharge activity of neuron model.And by changing the parameters to control the stable firing of the neuron system.First,based on the improved HR(eHR)neuron system,the equilibrium point of the system was firstly calculated.By using the stability theory to analyze the equilibrium point stability under different external stimuli.Then,theHopf bifurcation point of the system is determined by Matcont and the type of the point is determined.The bifurcation mode of the system is studied by time response diagram,phase trajectory map,single parameter and double parameter bifurcation diagram.When the external stimulus remains constant,the system has different discharge characteristics under different initial values.In order to further control the hidden discharge behavior of the system,Washout filter is applied to the system to realize the purpose of controlling the hidden discharge of the system and to change its discharge characteristics.Secondly,the mHR neuron system is taken as the research object to study its equilibrium point and Hopf bifurcation,and the bifurcation mode under single parameter and double parameter change of the system is studied by using Matlab software,the dynamic behavior of the system are analyzed emphatically.Then,in order to study the effect of energy on the firing law of the neuron system,by using theHelmholtz theorem,Hamilton energy control is applied to the neuronal system.The change of the discharge mode before and after the control is compared and explained,and the effect of Hamiltonian energy on the discharge law of the system is explored.Thirdly,magnetic flux is introduced into the mHR neuron model,namely the magnetic flux mHR neuron system.The discharge characteristics of neuron system under electromagnetic induction were studied.By using Routh-Hurwitz analysis,the condition of asymptotically stable equilibrium point of the system is obtained,and the bifurcation diagrams of the single and two parameters and the maximum Lyapunov exponential diagram.of the magnetic flux mHR neuron system were simulated by numerical simulation.The high-period discharge and chaotic discharge regions of the system are identified by the maximum Lyapunov exponential graph.Then,the effect of Hamiltonian energy on the firing mechanism of the flux neuron system was considered.This provides a reference for further research on the effect of energy on the firing behavior of neurons.