Spiral Waves Dynamics In A Two-layer Hindmarsh-Rose Neuronal Network Model

The emergence of neuronal dynamic models has greatly promoted the development of neuroscience.In 1952,Hodgkin and Huxley established the Hodgkin-Huxley model,which pushed the study of neuronal dynamics to a new height.Subsequently,many improved models based on the Hodgkin-Huxley model appeared,among which the Hindmarsh-Rose model is one of the excellent representatives of many improved models.In this paper,the Hindmarsh-Rose model is used to construct a two-layer neural network,and then the dynamic behavior of the two-layer neural network is studied.The real nervous system is composed of a large number of neurons constructed in different topologies,and there are a large number of different kinds of synapses used to transmit information between neurons.These factors make neural network become a complex organic system which can accurately process all kinds of information from the outside world.Electromagnetic field can change the transport and distribution of charged ions in neuron cells,and produce time-varying induction field and current,which has an important influence on the selection of action potential and discharge mode of neurons.In this paper,the dynamic behavior of a two-layer Hindmarsh-Rose neural network model is studied by using nonlinear(random)dynamics method and numerical simulation technique.In the first chapter,firstly,the research status and progress of the excitable cell coupling system network and synchronization are briefly described,including the synchronization of the coupled neurons,and the research on the coupled nerve cells at home and abroad.Secondly,the development of nonlinear dynamics and the important role of nonlinear dynamics in the study of the nervous system are introduced,and the nonlinear dynamics models of several common neurons.Finally,the basic knowledge of related theories used in this paper is briefly introduced,including complex network theory and nonlinear dynamics theory.In the second chapter,the Hindmarsh-Rose neural model and the nearest neighbor coupling method in complex network theory are used to construct a two-layer neural network.The two-layer network is connected to each other by means of electrical synaptic coupling,and this connection is not confined to a single area.The two layers are interconnected in one,three and four different areas respectively.In the first layer of the network,the spiral wave can be induced by the random initial value of the boundary,and in the second layer,the spiral wave can also be generated under appropriate conditions.In the third chapter,the noise-like is added to the Hindmarsh-Rose model as a variable of the electromagnetic field,and a model containing the electromagnetic field is constructed.Using the new model,a new two-layer neural network is established.The two layers of the network are connected by the electromagnetic field,and the connections are uneven and gradient.In the first layer of the network,the target wave is generated by different external excitation current.Under appropriate conditions,the generation of spiral wave can be observed in the two layers.The fourth chapter summarizes the main work in this paper,as well as the prospect of future research.Figure[32]reference[104]...