Dynamics Of Multi-Neurons Recurrent Inhibitory Loops With State-Dependent Time Delay

The study of the dynamic behaviors and the neurons firing laws of the neural network is an important means to reveal the mysterious functions of the brain in neurobiology. But topological structure of neurons is very complex, and the recur-rent inhibitory loop is only a kind of relatively simple structure. Supported by the National Natural Science Foundation of China "Dynamics and control of the state-dependent delayed system" under Grant NO.11372282 and based on the research of dynamics of the recurrent inhibitory models of two and three neurons, we further study the dynamics of them of four and five neurons.In this dissertation, we study the dynamics of four-neuron and five-neuron recur-rent inhibitory loops with state-dependent propagation time delay, incorporating a firing process and an absolute period is considered. Time delays are intrinsic proper-ties of the nervous systems due to axonal conduction time, distance of interneurons, finite switching speeds of amplifiers. The interaction among the synaptic time lag, the inhibitory feedback, the firing process and the absolute refractory period in these loops can give rise to enormous periodic patterns.the inhibitory postsynaptic poten-tial is regarded as a self-feedback of neuron E1 by introducing additional propagation delays, which is dependent on each of the basic oscillation of periodic patterns. In addition, we can divide periodic patterns into four cases, and obtain some theoreti-cal results of the four types of periodic patterns and validate the existence of some periodic patterns by numerical simulations with the variation of the synaptic time lag.The results show numerous periodic patterns can be obtained and the coexis-tence of a great deal of stable periodic patterns can be also taken birth. with the increase of the neurons, the number of periodic patterns of the corresponding system also increases and the effect of Synaptic delay is more remarkable, so the recurrent inhibitory systems with more neurons behave more complex dynamics.