THE NUMBER OF LIMIT CYCLES OF THE FITZHUGH NERVE SYSTEM

被引：0

作者：

Chen, Hebai

Xie, Jianhua

机构：

[1] Chengdu, Sichuan,610031, China

[2] Department of Mechanics and Engineering, Southwest Jiaotong University, China

来源：

QUARTERLY OF APPLIED MATHEMATICS | 2015年 / 73卷 / 02期

基金：

美国国家科学基金会;

关键词：

FitzHugh nerve system; limit cycle; Lienard system; LIENARD EQUATIONS; UNIQUENESS; DEGREE-4; PERTURBATIONS; LOOP;

D O I：

10.1090/S0033-569X-2015-01384-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we give a complete analysis of the number of limit cycles of the FitzHugh nerve system. First, we prove the uniqueness of the limit cycle when the unique equilibrium is a source. We then show that the system has two limit cycles if the unique equilibrium is a sink and limit cycles exist. We will also show that the mathematical study of limit cycles for FitzHugh nerve systems is related to Hilbert's 16th problem and is therefore an important area of study.

引用

页码：365 / 378

页数：14

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