Dynamics of Hindmarsh-Rose diffusive system

被引：0
|
作者：
Pan, Cuiyu [1 ]
Liu, Aimin [2 ]
Liu, Yongjian [2 ]
机构：
[1] Guangxi Normal Univ, Sch Math & Stat, Guilin 541000, Peoples R China
[2] Yulin Normal Univ, Ctr Appl Math Guangxi, Guangxi Coll & Univ Key Lab Complex Syst Optimiza, Yulin 537000, Peoples R China
来源：
NONLINEAR DYNAMICS | 2025年 / 113卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Hindmarsh-Rose diffusive system; Geometric singular perturbation theory; Periodic traveling wave; Canard explosion phenomenon; Relaxation oscillation; SINGULAR PERTURBATION-THEORY; CHAOTIC SYNCHRONIZATION; MODEL; POINTS; DELAY;
D O I：
10.1007/s11071-024-10285-8
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper, we discuss complex dynamic behaviors of Hindmarsh-Rose diffusive system (HRDS). Using traveling wave transformation, we firstly transform HRDS to slow-fast system with two small parameters. Applying geometric singular perturbation theory, we prove the existence of canard explosion phenomenon and relaxation oscillation in the slow-fast system. Thus, we get the existence of periodic traveling wave of HRDS. Furthermore, base on above theoretical result, we explain various firing activities of neurons.
引用
收藏
页码：1623 / 1635
页数：13
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