关于三维不可约合作系统的平衡点与周期轨道

Equilibrium points and periodic orbits of irreducible cooperative systems in R^3

研究三维不可约合作系统的平衡点和周期轨道存在性问题,得到新的存在判别准则:设K是此系统的一个闭轨线,则(a)系统一定存在两平衡点p,q满足p<q;(b)开序区间[[p,q]]一定含有一个平衡点u,使其在关系〈或〉意义下与闭轨道K不相关;(c)集合A(K)中一定含有一个不平衡点v.同时,还特别给出此系统平衡点、周期轨道和周期轨道稳定流形之间的关系.

In this paper we present new criteria for existence of equilibrium points and cycles for 3 - dimensional system that is irreducible cooperative. Particular attention is given to the relations of equilibrium points, cycles K and the stable manifold of K. Let be a closed orbit. Then ： （a） There exist two points p, q ∈ E such thatp 〈 q ;（b） [ [p,q] ] contains an equilibrium u which is unrelated to any point ofKby 〈 or 〉 ;（c） There exist an equilibrium v∈ A（K） which is unstable. Meanwhile, we give the relations among equilibrium system,cycle and manifold.