| The nervous system is a huge and complex information network composed of hundreds of millions of neurons,its intrinsic information transmission and electrical discharge process have always been a concern.Its rhythm is affected by various factors(such as electromagnetic radiation,synaptic type,system parameters,coupling mode,etc.).The change produces nonlinear dynamic phenomena such as bifurcation and synchronization.For such influencing factors,this thesis uses theoretical analysis and numerical simulation to investigate the firing rhythms and synchronous transitions processes of coupled element systems,and analyzes the spatiotemporal dynamics of complex neuronal networks,providing a theoretical basis for the study of neurobiology and modern neuroscience.The main contents of this thesis are as follows :In the first part,based on the improved ML neuron model,considering the effect of electromagnetic radiation,a magnetically controlled memristor is added to construct an electrically and chemically coupled memristive ML neuron model and an electrically and chemically coupled memristive ML ring network.The bifurcation processes of the two systems are studied separately by numerical simulation,and the synchronization of the two systems is analyzed quantitatively by similarity function and cross correlation coefficient.It is found that the electromagnetic excitation and coupling strength have effects on the synchronization of both systems.By changing the initial value of the ring neuron,the wave propagation is excited,and changing the system parameters can also change the wave propagation range,so as to control the dynamic behavior of the neuron cluster.In the second part,the equilibrium point stability of a single memristive HR neuron and an electrically coupled memristive HR neuron system is analyzed.Considering the electromagnetic radiation environment,an HR neuron model containing different types of coupling forms is established.By studying the linear coupling model and the nonlinear coupling model with the change of external stimulus current,the dynamic behavior from periodic oscillation to chaotic discharge is observed.ISI bifurcation diagrams,phase diagrams,and coupled neuron time series diagrams are obtained by numerical simulations.it is found that when the coupling form shifts from linear to second-order nonlinear,the discharge mode of the coupled neuron system becomes simple.In the third part,a double-layer memristive HR ring neural network and a double-layer memristive HR grid neural network are established.The discharge rhythms of the neural network under the effect of intra-layer electrical coupling strength,inter-layer electrical coupling strength,and electromagnetic excitation are investigated.It is shown that the electrical coupling strength has a regulatory effect on the discharge mechanism of the neuron network.In addition,the evolution of the neuronal membrane potential of the network under different external conditions or interlayer coupling strength is demonstrated by using the spatiotemporal wave diagram of network cluster behavior.It is found that the stimulation of the initial value can make the transition from the synchronous to the asynchronous discharge state of the doublelayer ring neural network,and the appropriate increase of the interlayer electrical coupling strength is beneficial to the propagation of the target wave in the double-layer lattice network. |
