Study On Synchronization And Collective Dynamics Analysis Of Memristor Neural Network

As the basic unit of the brain nervous system,neurons are interlinked with other neurons within the nervous system to achieve specific activities.In recent decades,a large literature on neurodynamic research combining neurophysiology and nonlinear dynamics has emerged both at home and abroad.Since then,with the emergence of memristors,they have been used by a wide range of researchers for the study of complex neural networks because of their inherent superior properties.Compared with traditional neural networks,neural networks containing memristors(referred to as memristor neural networks)are better able to simulate the structure and function of the human brain,and have become a frontier research topic in the intersection of neuroscience,informatics,nonlinear dynamics and other multidisciplinary fields.Currently,with the continuous development of neuroscience,the types of neuronal models can be divided into continuous neuronal models represented by differential equations and discrete neuronal models represented by difference equations.In this paper,we focus on continuous type Izhikevich and Hindmarsh-Rose neuron models as the research object,based on complex networks and nonlinear dynamics theory and methods,to establish complex memristive neural network models,and then study the influence of network parameters on the collective behavior and synchronization of complex memristor neural networks.The specific research work of the paper is as follows:(1)Summarize the research background and significance of this topic,the history and progress of neuroscience and the current status of domestic and international research on the collective behavior of memristor neural networks,then the structure and basic properties of neurons,some classical neuronal models,and finally a brief introduction to the relevant theoretical knowledge of complex network models and amnestic devices to provide theoretical support for this paper.(2)The collective dynamics behavior of electromagnetic field coupled memristor Izhikevich neural network is studied.The effect of electromagnetic field is firstly considered,and electric field variables and magnetic flux variables are introduced into the Izhikevich neuron model to construct the neural network using electrical synaptic coupling,and then the effect of electrical synaptic coupling and magnetic field coupling on the collective dynamical behavior of the amnestic Izhikevich neural network is investigated.Numerical simulation results reveal that the neural network gradually reaches the synchronized state and the firing pattern of neurons changes as the strength of electrical synaptic coupling increases.Increasing the magnetic field coupling value can increase the firing activity of neurons and promote the network synchronization,while increasing the electric field suppresses the firing activity of neurons.In addition,when electrical synaptic and magnetic field coupling act together,the smaller the value of magnetic field coupling,the more effective electrical synaptic coupling promotes network synchronization;in the presence of electrical synaptic coupling,the electric field is more effective in suppressing electrical activity.The results are expected to provide new insights into the understanding of signal encoding and transmission in the nervous system.(3)To study the collective dynamics and synchronization behavior of memristor neural network with distance power-law control.First,a Newman-Watts small-world memristor Hindmarsh-Rose neural network with electrical coupling is constructed,and power-law exponents are introduced between neuron distances.Then,numerical simulation and statistical analysis are used to study the effects of the electromagnetic induction coefficient,the strength of electrical coupling and the power-law exponent on the collective dynamics of the Hindmarsh-Rose neural network.It is found that the electromagnetic induction coefficient and electrical coupling strength can change the firing pattern of neurons when the power-law exponent is zero;when the electromagnetic induction coefficient and electrical coupling strength are taken,the maximum synchronization of the network can be achieved.In the case of power-law exponent greater than zero,when the power-law exponent is small,increasing either the electromagnetic induction coefficient or the electrical coupling strength can enhance the network synchronization;when the power-law exponent is large,the electromagnetic induction coefficient takes the appropriate value to achieve a higher synchronization of the network,while increasing the electrical coupling strength has little effect on the network synchronization.In addition,it is found that at low power-law exponents,the memristor neural networks can exhibit non-coherent,chimera,multi-chimera and coherent states.Results analysis is expected to provide useful guidance for studying neural networks to obtain more information about synchronization behavior and chimera states.(4)To study the collective dynamic behavior of multilayer memristor neural networks under electromagnetic induction.Firstly,a two-layer Newman-Watts small-world neural network is established,the first layer is memristor Hindmarsh-Rose neural network and the second layer is memristor Izhikevich neural network,in which electrical synaptic coupling is used within the layers and memristor coupling is used between the layers.Then,the order parameter,standard deviation,synchronization factor and interlayer error are introduced to measure the orderliness,discharge strength and synchronization of the two-layer network.The electrical synaptic coupling and the memristor coupling are used as control parameters to study the collective behavior of the multilayer memristor neural network.The results showed that at low values of interlayer memristor coupling,the enhancement of intralayer electrical synaptic coupling values could change the firing pattern of the amnestic neural network and produce repolarization;at larger values of interlayer memristor coupling and intralayer electrical synaptic coupling,the neurons showed early repolarization,while the multilayer memristor network showed an ordered,low-activity amplitude death state;it was also found that when the multilayer memristor network was amplitude death It was also found that the interlayer synchronization was strongest when the multi-layer amplitude death state was present.The results provide a possible method to control the firing mode shift and amplitude death phenomenon by adjusting the memristor coupling and electrical synaptic coupling.