Bifurcation Mode And Control Of Neuron Models Under Electromagnetic Induction

In this thesis,the discharge modes of two types of neuron models with bistable characteristics under the action of electric and magnetic fields are studied,the evolution law of the hidden discharge and the control strategy are analyzed by using Matcont,XPPAUTO and nonlinear dynamics theory.The influences of the system parameters,including external stimulus current,electromagnetic induction intensity and flux feedback gain,on the global bifurcation structure,coexisting attractor and its attraction domain of the neuron model under complex electromagnetic radiation modulation are discussed based on the single-parameter and two-parameter bifurcation analysis.The main research contents are as follows:1.The flow of large amounts of ions in the nervous system(e.g.,potassium,sodium,and calcium ions)will stimulate time-varying electric fields,which can further regulate the firing activity of neurons.The discharge activity and global bifurcation modes of Hindmarsh-Rose(HR)neuron model with bistable characteristics under electric field were studied using numerical simulation and the corresponding Hopf bifurcation theory.The global attraction domain of the model is analyzed by using Matcont and its programming,and it was found that the model had coexistence mode oscillation and hidden discharge behavior caused by subcritical Hopf bifurcation.In addition,the unstable branches are effectively controlled based on the Washout controller,thus the hidden discharge is eliminated.Interestingly,by two-parameter bifurcation analysis,it is also found that the model generally has a“comb-shaped” chaotic structure and a period-adding bifurcation with and without chaos.It is noteworthy that considering the electric field is inevitably disturbed by external periodic disturbances,which will lead to more complex discharge modes and abundant coexisting discharge modes.2.An e-HR neuron model with mixed oscillating modes was established based on the coupling of flux variables to the neuron membrane potential by using a magnetocontrolled memremor.The distribution of the equilibrium point and its bifurcation properties in the e-HR model are discussed in detail.It is found that there are subcritical Hopf bifurcation,coexisting oscillating modes and periodic hidden attraction in the model.It is noteworthy that the subcritical Hopf bifurcation point of this model can be transformed into supercritical Hopf bifurcation point by applying Washout controller.Meanwhile,the hidden oscillation behavior is effectively eliminated.In order to analyze the influence of various parameters on the bifurcation behavior,numerical simulation tools such as single-parameter bifurcation diagram,two-parameter bifurcation diagram and maximum Lyapunov exponent diagram are using to show that the model has complex discharge behavior and periodic bifurcation mode based on a large number of numerical results.Furthermore,the periodic cluster discharge states and mixed-mode oscillations(OR MMOs)will result in a discontinuous ‘periodic dislocation layer' bifurcation structure on the corresponding two-parameter plane.Interestingly,the periodic cluster discharge state of the model can be transformed into MMOs mode when system parameters are subject to random perturbations.3.Combining the fast dynamic variable of Wilson model,slow dynamic variable of Hindmarsh-Rose model and state-dependent electromagnetic induction effect,a four-dimension hybrid neuron model with multistable is established,then its discharge activity and bifurcation law are studied by global bifurcation analysis.In detail,when the electromagnetic induction intensity does not depend on the change of membrane potential threshold,the global stability of the model and its Hopf bifurcation and saddle node bifurcation behaviors on a two-parameter plane are discussed based on Matcont software.In addition,through the bifurcation diagram and its corresponding maximal Lyapunov exponent diagram,a large number of numerical studies show that the model has a period-adding bifurcation with and without chaos and a comb-shaped chaotic structure.Interestingly,when the electromagnetic induction intensity depends on the change of membrane potential threshold,the original smooth hybrid neuron model is transformed into a non-smooth switching(Filippov)system under the control of membrane potential threshold.Meanwhile,the existence and stability of the equilibrium point of this switching system are discussed.It is noteworthy that the threshold of membrane potential has a destructive effect on the comb-shaped chaotic structure.Accordingly,it is found that the switching system has the coexistence of multiple attractors,and the spatial and temporal distribution of coexisting attractors is analyzed in detail based on simulation methods such as phase trajectory,Poincare section and attraction domain.The research results of this paper will provide a useful discussion for neural computing science and artificial intelligence network design.