Dynamic Analysis,Bifurcation And Synchronization Control Of Fractional-order Magnetic Flux ML Neuron Model

When neurons have abnormal bifurcation or abnormal synchronization,it will cause some neurological diseases.Considering the fractional-order differential form and the neuron model under the condition of electromagnetic induction feedback can help us to better understand the complex dynamic behavior of neurons,which has far-reaching practical significance to promote the study of neurological diseases.In this paper,the fractional-order theory and the magnetic flux Morris-Lecar(ML)neuron model are combined to establish the fractional-order magnetic flux ML neuron model to analyze and simulate the bifurcation and synchronization dynamics of neurological diseases,and the corresponding controller is designed to control the bifurcation and synchronization of the fractional-order magnetic flux ML neuron model.The main work of this paper is as follows:1.Taking the external stimulated current as the control parameter,the effects of order and electromagnetic induction feedback intensity on the bifurcation of fractionalorder magnetic flux ML neuron model are studied.Then,the synchronization behavior of fractional-order magnetic flux ML neurons is studied,and it is found that the increase of electrical synaptic coupling intensity can promote the synchronization of fractionalorder magnetic flux ML neuron model of electrical synaptic coupling,and the increase of memristor synaptic coupling intensity or magnetic flux initial value can promote the synchronization of fractional-order magnetic flux ML neuron model of memristor synaptic coupling.2.The integer-order Washout filter is extended to the fractional-order Washout filter defined by Caputo.According to the fractional-order nonlinear system stability criterion,the bifurcation control of the fractional-order magnetic flux ML neuron model is realized,which makes the system stable to the equilibrium point,and the convergence speed is faster than the integer-order Washout filter.Moreover,there is an appropriate control gain under any order to realize the stability control of the system,and the fractional-order Washout filter can also control the bifurcation point of the system to any desired position.3.Due to the parameter uncertainty of coupled fractional-order flux ML neuron model,an adaptive controller based on Lasalle invariant set is designed to synchronize the fractional-order flux ML neuron model with electrical synaptic coupling and memoir synaptic coupling.The controller can not only estimate the unknown parameters,but also adjust the control gain automatically.Then,considering the influence of noise in the coupled system,a more robust sliding mode controller based on hyperbolic tangent function is adopted,which effectively overcomes the influence of chattering and noise.The synchronization error converges to zero quickly and the steady-state performance is good when two kinds of noisy fractional-order magnetic flux ML neuron models with different synaptic coupling are synchronized.The simulation results verify the effectiveness and feasibility of the two designed synchronization controllers.