The Influence Of Autapse On Synchronous Firing In Small-world Neural Networks

Analyzing and understanding the features and functions of the most important organ,the brain of humans,are of the most challenging and leading edge in the 21^stcentury.Research on modeling neural network dynamics is an important strategy of the 14^th Five-Year Plan for China.Clinical studies demonstrate that synchronization of the nervous system is strongly related to diseases such as Parkinson’s disease,Epilepsy,Schizophrenia,and so on.Both theoretical and experimental studies suggest that an abnormal synapse in neurons,the autapses,plays a crucial role in the firing and synchronization of neurons in neural networks.Although previous theoretical studies have found that autapses regulate the electrical activities of single neurons and the synchronization of neural networks,which focuses on the effects of autapses on single neurons and neglects the synaptic time delay between neurons.In this thesis,we focus on the effect of autapses on the synchronous firing of small-world neural networks.We hope it could provide some theoretical support for future studies on neural synchronization mechanisms and disorders such as Parkinson’s disease,Epilepsy,Schizophrenia,and so on.This thesis is based on the Hodgkin-Huxley model for modeling the electrical activities of single neurons.A small-world topological structure is used to build connections between neurons.This thesis reflects the dynamics of autapses in neural networks by modeling the impact of different types of autapses on the synchronous release in neural networks.It is found that:（1）As the external stimulus current decreases,the neural firing rate of single neurons gradually decreases,and no more action potentials are generated when it reaches a threshold.In the small-world networks without autapses,the system shows a synchronization transition as the time delay increases.The neural firing pattern strongly depends on the given parameters,which can present patterns,such as completely synchronous,and so on.As time delay changes,the neural firing patterns transform from nonlinear to oscillating.（2）Various types of autapses have inhibitory effects on neural firing patterns under specific parameters and modulate the synchrony of neural firing patterns.Within characteristic regions,neural discharges can be completely inhibited,forming inhibitory zones.In certain conditions,the autapses have a decisive influence on the neural firing patterns,which is in agreement with the relevant experimental findings.The results of the numerical simulations in this thesis qualitatively coincide with previous related experiments,and the study provides theoretical support for revealing the critical role played by autapses in determining the complex dynamics of nerves and the formation of neurological diseases.The thesis has 41 figures,1 table and 127 references.