Bifurcation Analysis And Control Of The Neuron Model

The nervous system contains a network of neurons that regulate and coordinate all of the physiological processes within our bodies.A breakdown in the coordination and control of the nervous system leads to an abnormality and a disorder in the underlying physiological control mechanism,resulting in the occurrence of many neurological diseases such as epilepsy,Alzheimer's disease,Parkinson's disease,or schizophrenia.From the viewpoint of nonlinear dynamical systems,these diseases can be considered to be caused by a bifurcation induced by a change in the values of one or more regulating parameters in the relevant nonlinear equations describing the neuronal system.Therefore,an in-depth study of the generation and control of bifurcation has a potential application for the diagnosis and treatment of these dynamic diseases.A washout filter-aided dynamic feedback controller has been applied to a variety of nonlinear dynamic model.In this paper,the mechanism leading to a bifurcation of Morris-Lecar(ML)model is studied by employing the nonlinear dynamical theory and methods,and washout filter is used to control the bifurcation.This controller composed of the linear term and the nonlinear cubic term,where the linear term is shown to determine the location of the Hopf bifurcation,while the nonlinear cubic term regulates the criticality of the Hopf bifurcation.This paper then analyzes the relationship between the externally applied current,the linear control gain,the nonlinear control gain,and the reciprocal of the filter time constant.Through these relationships,we can select the appropriate parameter values to achieve our control objectives.This paper also analyzed the relationship between the controllable parameters of the neuron system and the externally applied current.By adjusting the parameter values of the controllable parameters without adding any control,we can change the position of the Hopf bifurcation point and even change the excitatory type of neurons.Compared to the method adding controller to change these features,this method will not increase the system dimension to make the system more complex.The above research results of analysis and control contribute to revealing nosogenesis of some neuronal diseases,and provide some theoretical support for prevention and treatment of some neurological diseases.It has certain guiding significance in the application of clinical medicine.