Firing Characteristic Analysis And Synchronization Control Of Neuronal Model With Magneto-acoustical Stimulation Input

Transcranial magneto-acoustical stimulation(TMAS)is considered as a potentially effective treatment for neurological disorders as its advantages in terms of spatial resolution and penetration depth.Nowadays,the research on TMAS is mainly carried out through theoretical analysis and animal experiment,and still require a large amount of basic work as the guideline for clinical application.The neuronal model with magneto-acoustical stimulation input can simulate the electrical activities of neurons stimulated by TMAS.The research on the firing properties and synchronization control of the neuronal model with magneto-acoustical stimulation input contributes to the understanding of the mechanism of TMAS and the discharge characteristics of the nervous system under magneto-acoustical stimulation.Given this,this thesis investigates the firing characteristic and synchronization control of the neuronal models with magneto-acoustical stimulation input,and the main research contents are given as follows:(1)For the spike-frequency adaptation characteristics of the Ermentrout neuronal model with magneto-acoustical input,the effects of the different magnetic field and ultrasonic parameters on neural spike-frequency adaptation are analyzed.Firstly,based on the simulation experiment,the membrane potential curves and spike-frequency curves under different magnetic field and ultrasonic parameters are generated,and the effect of these parameters on the adaptation process of the neuron are analyzed.Moreover,the adapted onset spike-frequency curves with different input parameters and initial values of the adaptive variable are exhibited to investigate the effect of the different magnetic field and ultrasonic parameters on the neural spike-frequency adaptation.Finally,the physiological mechanism of the conclusions is discussed.(2)For the firing characteristic of the fractional-order extended Hindmarsh-Rose(HR)neuronal model with magneto-acoustical stimulation input,the effect of the different magnetic field and ultrasonic parameters on the firing mode and firing rhythm of the neuronal model are investigated.Firstly,the fractional-order extended HR neuronal model which has been verified to be more consistent with the biological characteristics of a neuron is considered.Based on the simulation experiment,the membrane potential curves under different magnetic field and ultrasonic parameters,and the corresponding interspike interval diagrams are generated and analyzed,then the firing modes and firing rhythms of the neuronal model with the different magnetic field and ultrasonic parameters are concluded.In addition,the complex dynamic properties of the fractional-order neuronal model are explored by comparing the interspike interval diagrams of the membrane potential curves of the fractional-order neuronal model to those of the integer-order neuronal model.(3)For the synchronization for the fractional-order extended HR neuronal model with magneto-acoustical stimulation input,an adaptive neural network controller is designed to achieve the synchronization control of the master-slave system of neuronal models.Based on the fractional-order definition and properties,a new sliding surface is introduced to construct the synchronization error system of the master and slave neuronal models.Considering the nonlinearity and uncertain parameters of the neuronal model as well as the unknown external disturbances,an adaptive neural network slide mode control scheme is proposed to make the slave neuron realize resilience for the uncertain parameters and the external disturbances,and achieve synchronous rhythms of the membrane potentials with those of the master neuron.(4)For the generalized projective synchronization for the fractional-order extended HR neuronal model with magneto-acoustical stimulation input,an adaptive fuzzy controller is designed to achieve the generalized projective synchronization control of the master-slave system of neuronal models.Based on the master and slave neuronal model with different fractional orders,new synchronization errors are introduced to construct the generalized projective synchronization error system.Considering the uncertain parameters of the neuronal model and the unknown external disturbances,an adaptive fuzzy generalized projective synchronization control algorithm is designed.By choosing the appropriate design parameters,the proposed control scheme enables the master-slave neuron system to achieve complete synchronization,anti-phase synchronization,and generalized projective synchronization in a finite amount of time and to be resilient to uncertain parameters and unknown disturbances.(5)For the prescribed performance synchronization of the Hodgkin-Huxley(HH)neuronal model with magneto-acoustical stimulation input,an adaptive neural network controller is designed to achieve the prescribed performance synchronization of the masterslave system of the HH neuronal models.By taking the different model parameters of the master and slave neurons into consideration,a new filter error is introduced by state transformation to make the equivalent unconstrained stabilization control problem instead of the constrained tracking problem.A stable adaptive neural network synchronization controller is designed to overcome the nonlinearity and uncertainties of the neuronal model and ensure the synchronization status of the master and slave neurons,as well as the prescribed synchronization performance in the processes of synchronization.