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

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.