In this paper we analyze globally the behavior of the solutions of a class of cooperative systems. Our main results is that every orbit of the cooperative system (3.1) either approaches the equilibrium (0, 0, 0), or i...In this paper we analyze globally the behavior of the solutions of a class of cooperative systems. Our main results is that every orbit of the cooperative system (3.1) either approaches the equilibrium (0, 0, 0), or is unbounded, ast→+∞.展开更多
Hirsch[1,2] studied the limiting behavior of solutions of competitive or cooperative systems, and showed that ifL is an ω-limit set of a three-dimensional cooperative system, which contains no equilibrium, thenL is a...Hirsch[1,2] studied the limiting behavior of solutions of competitive or cooperative systems, and showed that ifL is an ω-limit set of a three-dimensional cooperative system, which contains no equilibrium, thenL is a nonattracting closed orbit. Smith<sup class='a-plus-plus'>[3]</sup> considered a three-dimensional irreducible competitive system and showed that an ω-limit set containing no equilibrium must be a closed orbit which has a simple Floquet multiplier λ<1, and may be attracting. In this paper we carry out the qualitative analysis of a class of competitive and cooperative systems, and a generalization of the result of Levine<sup class='a-plus-plus'>[4]</sup> is given. The stability problem of closed orbits raised in [5] and [6] is resolved.展开更多
基金This is a part of my Master thesis under the direction of Professor Li Bingxi.
文摘In this paper we analyze globally the behavior of the solutions of a class of cooperative systems. Our main results is that every orbit of the cooperative system (3.1) either approaches the equilibrium (0, 0, 0), or is unbounded, ast→+∞.
文摘Hirsch[1,2] studied the limiting behavior of solutions of competitive or cooperative systems, and showed that ifL is an ω-limit set of a three-dimensional cooperative system, which contains no equilibrium, thenL is a nonattracting closed orbit. Smith<sup class='a-plus-plus'>[3]</sup> considered a three-dimensional irreducible competitive system and showed that an ω-limit set containing no equilibrium must be a closed orbit which has a simple Floquet multiplier λ<1, and may be attracting. In this paper we carry out the qualitative analysis of a class of competitive and cooperative systems, and a generalization of the result of Levine<sup class='a-plus-plus'>[4]</sup> is given. The stability problem of closed orbits raised in [5] and [6] is resolved.
