Research On Nonlinear Response Of Magnetic Flux-coupled Neuronal System

With the continuous development and progress of neuroscience,electrical activities in neuronal models and biological experiments have been extensively studied,to discover the underlying mechanisms of information encoding and signal processing in the nervous system.The nervous system is made up of a large number of neurons,and excitatory neurons and inhibitory neurons are essential to activate appropriate electrical activity patterns.A real biological neuron is complex and often exhibits a variety of electrophysiological activities,ion diffusion and proliferation in the cell.Many neuron models have been proposed to reproduce this electrical activity behavior.However,single neuron can rarely complete the encoding and transmission of information,so the synchronization of coupled neuron system is the key to study signal transmission.Therefore,this paper mainly studies the bifurcation,synchronization and electrical activity behavior of the coupled neuron system from the aspects of mathematics and physics.Mathematical language is used to describe the diverse dynamic behaviors of complex neural systems,which provides a theoretical basis for the research fields of neuroscience and medicine.The main research contents and methods are as follows:First and foremost,based on the improved Hindmarsh-Rose neuron model,namely the magnetic flux neuron model,the dynamic behavior about the electrical activity of the neuron under electromagnetic induction is discussed.By changing the parameters or selecting the appropriate external stimulation current,various discharge states of the electrical activities of neurons can be obtained.In addition,the dynamic analysis of the neuron model with magnetic flux is carried out.For example,the existence of Hopf bifurcation is discussed with the Hopf bifurcation theorem.The discharge characteristics of neurons are discussed by time response diagram,phase diagram and bifurcation diagram,and the rich dynamic characteristics of the model are demonstrated.Then,based on the fluxion neuron system,two fluxion neurons are coupled by fluxion coupling method,and the coupling neuron model is established.First,the Routh-Hurwitz criterion is used to analyze the stability of the system equilibrium point and A unique equilibrium point is calculated.Secondly,the bifurcation analytical solution is obtained by Hopf bifurcation theorem,and the bifurcation direction of the system and the stability of the bifurcation periodic solution are studied.Finally,the bifurcation diagram and time response diagram of the system under a single parameter change were studied by numerical simulation,and the influence of coupling strength on the bifurcation behavior and discharge mechanism of the system is investigated.Finally,Gaussian white noise is introduced into the coupled neuron model to explore the electrical activity pattern and synchronization behavior of neurons under electromagneticradiation.According to the module analysis method,the system is transformed into a linear system,In other words,the synchronization problem of two neurons is transformed into the negative qualitative problem of matrix,and sufficient and unnecessary condition for the synchronization of two flux neurons is obtained.The synchronization error graph of flux-coupled neuron model under the action of system parameters and coupling strength is obtained by MATLAB numerical simulation,and the influence of coupling strength on the model synchronization is discussed.Then,the synchronization behavior of coupling neurons under the external magnetic field is studied.The effect of coupling strength promotes the system to reach the synchronous state,which provides a theoretical basis for the effective transmission of confidential information.