| A large number of neurophysiological studies have shown that the dynamic behavior of neurons closely affects the complex behavior of human brain.There are many complex and abundant chaotic discharge behaviors among neurons,which are an interesting nonlinear dynamic phenomenon.In order to further understand the activity of biological neurons,a variety of neuron models have been established,and a variety of neural network topologies have been established according to different types of synapses and connection modes to simulate and study the main dynamic characteristics of biological neurons.Neural network is a large and complex nonlinear dynamic system,which is an information network formed by many neurons connected by synapses.Hindmarsh-Rose(HR)neurons have been studied widely because of their simple structure and their ability to reflect the complex electrical activity of biological neurons.Based on the three-dimensional HR neuron model,functional neural model,memristor neural model and high-dimensional neural network model are constructed in this thesis.Different discharge modes,bifurcation behaviors and synchronous transition processes of the nervous system are observed by numerical simulation.The main research contents are as follows:1.A four-dimensional neuron model with Josephson junction is constructed by introducing Josephson junction into HR neuron.Firstly,the dissipative property of the system and the stability of the equilibrium point are obtained through theoretical analysis.The bifurcation of the electric-coupled system is observed by adjusting Josephson junction parameters,and it is found that the system exhibits rich dynamic characteristics such as period-doubling bifurcation and period-adding bifurcation including chaos in the appropriate parameter range.A global coupled neural network is constructed under the action of chemical synapses.Synchronization factors are used to describe the synchronization degree of the system under different parameters.It is found that coupling intensity and Josephson junction parameters could affect the discharge synchronization state of the system.2.Two different types of memristors are added to HR neurons to construct two HR nervous systems with different memristors,namely magnetically controlled memristor nervous system and hyperbolic memristor nervous system.By depicting the single parameter and double parameter bifurcation diagrams to analyze the discharge transition process of different memristor neurons,it can be found that the system presents more diversified discharge modes under the control of memristor parameters.A memristor coupling model is constructed by chemical synaptic connection,and the effects of chemical coupling strength and memristor parameters on the synchronization of the system are observed,and the appropriate range of parameters is further determined.3.Based on the ring network topology,the double-loop network and the three-layer ring network models are constructed respectively.Double-loop network is a double-loop topology formed by two identical loops sharing a central neural node.Under this model,the regulation effects of excitatory and inhibitory chemical synapses on the discharge rhythm of the network are explored respectively,and the parameter values of the reversible potential of chemical synapses are determined through comparative analysis,providing parameter support for observing the discharge bifurcation behavior of the system with changes in other parameters.Three-layer ring network is three identical rings through cross-layer coupling in space to achieve the multi-layer network topology.The process of discharge transition is observed,and the changes of membrane potential generated by partial stimulation of the neural network are shown through the space-time wave diagram.The formation and extinction of the traveling wave of the system are explored by taking the initial value,coupling strength,external current and other factors as the stimulus variables of a specific region. |
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