Existence and stability analysis of homoclinic cycle and periodic solution of quartic integrate-and-fire neuron model

被引：0
|
作者：
Wu J. [1 ]
Xu J. [1 ]
Wang J. [1 ]
Xu Q. [1 ]
机构：
[1] School of Mathematics and Information Sciences, Guangxi University, Nanning
来源：
Zhendong yu Chongji/Journal of Vibration and Shock | 2023年 / 42卷 / 23期
关键词：
1-order homoclinic cycle; 1-order periodic solution; homoclinic bifurcation; impulse effort; quartic integrate-and-fire neuron model;
D O I：
10.13465/j.cnki.jvs.2023.23.025
中图分类号：
学科分类号：
摘要：
Here, the existence and stability of periodic solution of a quartic integrate-and-fire (IF) neuron model system with impulse effect (state reset process) were studied by analyzing its homoclinic bifurcation. Qualitative analysis was performed for dynamic behavior near saddle points of the system with two equilibrium points, and the existence of 1 -order homoclinic cycle of the system was studied in various cases. The existence and stability of 1-order periodic solution near 1-order homoclinic ring in different cases were proved by using the impulsive dynamic systems theory and the fixed-point theory of Poincare map when the system has homoclinic bifurcation with d taken as bifurcation parameter. Finally, the periodic solution of the system was numerically simulated to verify the correctness of theoretical results. It was shown that the method used here can provide a strategy for finding periodic solution of impulsive dynamic systems. © 2023 Chinese Vibration Engineering Society. All rights reserved.
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页码：209 / 214
页数：5
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