FitzHugh神经系统中的无穷远奇点及闭轨的存在性  

Degenerate Equilibria at Infinity and the Existence of Closed Orbit in the FitzHugh Nerve System

作　　者：陈和柏[1] 石勇国[2] 

机构地区：[1]四川大学数学学院,四川成都610064 [2]内江师范学院数学与信息科学学院,四川内江641112

出　　处：《四川师范大学学报（自然科学版）》2013年第1期18-22,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11101295);四川省教育厅自然科学重点基金(12ZA086)资助项目

摘　　要：研究了一类多项式生物系统的定性性质.通过研究沿特殊方向轨线的数目和走向来分析无穷远奇点的定型性质,并且对一类特殊情形b=0给出了FitzHugh神经系统中闭轨的存在唯一性条件.In this paper we consider a polynomial differential system, which was given from the squid giant axon membrane. By determining characteristic directions and the numbers of orbits which go towards or away from those equilibria in characteristic direc- tions, we analyze qualitative properties of its equilibria at infinity. For b = 0, we give necessary and sufficient conditions for existence of closed orbits, and prove that the system has a unique closed orbit if it exists.

关 键 词：无穷远奇点 Ponincaré-Bendixson环域 Briot-Bouquet变换 Poincaré变换 正常区域 闭轨 LIÉNARD系统 

分 类 号：O192[理学—数学]