Study On Collective Dynamics Analysis And Control Of Memristor Neural Network

Neuron is the basic unit that constitutes the structure and function of the nervous system.The study of various electrophysiological phenomena of neurons is the basis for human understanding and exploring the mysteries of the brain.The electrical activity behavior of neurons depends on complex electrophysiological conditions.According to the law of electromagnetic induction,the change of membrane potential of neurons will produce magnetic field in the surrounding environment,and the change of external magnetic field will also affect the membrane potential of neurons.In the traditional neuron model,one-dimensional flux variables are introduced to describe electromagnetic induction in neurons.It has been shown that the nonlinear dynamic analysis and synchronous control of memristive neural network are of great significance to understand the signal coding and propagation mechanism of neural system.At present,there are few researches on collective dynamics and synchronous control of memristive neural networks with different models.In this paper,the Hodgkin-Huxley and Hindmarsh-Rose neuron models are taken as the research objects.Based on complex network theory and mathematical modeling method,a complex memristive network model is established to analyze the nonlinear dynamic behavior of the network and adjust the parameters to control the synchronization of the network.The research is divided into two parts: one is to analyze the collective dynamic behavior of neural network with electromagnetic field coupling;the other is to realize synchronous control of neural network by adjusting bifurcation parameters.The main work of this paper is as follows:First,summarize the domestic and foreign research status of collective firing activity and synchronous control of memristive neural network,and then take Hodgkin-Huxley and Hindmarsh-Rose as research objects to analyze the triggering conditions of the firing activity pattern transition.Finally,the theoretical knowledge of common complex networks and memristor models is briefly introduced,which provides theoretical support for this paper.Second,research on the firing activity of neural network with distance weight under the coupling of magnetic field.A small world Hodgkin-Huxley memristor neural network with magnetic field coupling is constructed,and the distance weight is introduced between neuron nodes.The influence of distance weight and system size on the discharge activity of neural network is studied by numerical simulation and statistical analysis.The research results provide a method to control the transformation of neural network discharge mode by adjusting system size and distance weight.Third,study the collective dynamic behavior and synchronization control of memristor neural networks under electromagnetic induction.The electric field variable E is introduced to describe the ion distribution caused by the exchange of ions in the cell and the sensitivity of the membrane potential,and a Hindmarsh-Rose memristive neural network considering both the electric field and the magnetic field is established.Using the methods of numerical simulation and statistical analysis,the focus is on the influence of electrical synaptic coupling strength,magnetic field coupling strength,and cell size on neuron firing patterns and network synchronization behaviors.The numerical results show that the effects of magnetic coupling strength and cell size on synchronization can be changed by changing the electrical synaptic coupling.On the other hand,with lower magnetic coupling strength and cell size,electrical synaptic coupling can induce synchronization more effectively.The results provide useful guidance for the study of signal propagation between neurons.Fourth,study the collective dynamics and synchronization control of multilayer memristive neural networks under electromagnetic induction.Taking the Hindmarsh-Rose neuron considering electromagnetic induction as the node,a two-layer small-world neural network is established,where electrical synaptic coupling is used in the layers,memristor coupling is used between the layers,and the two-layer networks are set to different discharge modes.Using the methods of numerical simulation and statistical analysis,the focus is on the influence of electrical synaptic coupling strength and electromagnetic induction coefficient on the collective behavior of neural networks.The results show that electromagnetic induction has an important effect on regulating the dynamic behavior of neural networks,and provides useful guidance for the study of physiological functions related to brain.