Open AccessThe number of limit cycles of the FitzHugh nerve system
Author(s) -
Hebai Chen,
Jianhua Xie
Publication year - 2015
Publication title -
quarterly of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.603
H-Index - 41
eISSN - 1552-4485
pISSN - 0033-569X
DOI - 10.1090/s0033-569x-2015-01384-7
Subject(s) - uniqueness , limit (mathematics) , algorithm , computer science , limit cycle , semantics (computer science) , control limits , mathematics , mathematical analysis , programming language , process (computing) , control chart
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 16 th ^{\mbox {th}} problem and is therefore an important area of study.