Stability And Hopf Bifurcation Of Ring Coupling Neural Networks

With the help of neuroanatomy,neuronal tracing and neuroimaging techniques,the presence of ring neural structures in neural tissues such as the hippocampus,cerebellum and cortex has been identified at an early stage,and the dynamics of ring neural networks has attracted extensive attention.Regrettably,most of the research on the ring structure network is limited to the single-ring structural model with few neurons.For instance,a double-coupled loop structure exists in cortico-basal gangliathalamo-cortical neural circuit.Therefore,it is clear that using only single-ring structures to probe the dynamic behavior of the ring neural network is not universal.In order to extend the dynamics of the ring neural network to a more general situation and reveal the patterns and underlying mechanisms of the functional activity of the ring nerves.From this biological background and previous research work on single-ring neural networks,this thesis proposes three types of ring-coupled neural network models(single-core dual-ring coupling model,single-core multi-ring coupling model,and dual-core ring coupling model),which mainly study the stability,bifurcation and synchronous oscillation dynamics of these models behavior.The specific work is as follows:1)A class of asymmetric dual-ring coupling neural network is proposed,the bifurcation behavior and oscillation properties of the dual-ring coupling neural network are studied,and the bifurcation threshold of the proposed model is given.2)A class of high-dimensional multi-ring coupling neural network model with discrete time delay is established,and the Coates flow graph method is introduced to obtain the characteristic equations of the high-dimensional network.The effects of time delay on the stability,bifurcation threshold,amplitude,period and node synchronization of the neural network are discussed.3)A class of dual-core loop coupling neural network model is designed to discuss the bifurcation threshold for switching from steady state to unstable state with time delay,the effect of time delay on the amplitude of the periodic oscillatory state,and the conditions for synchronizing the motion trajectories of similar nodes.