带有多滞量的Lotka-Volteraa三种群互惠系统的周期解

Periodic Solution of Lotka-Volteraa Facultative Mutualism System of Three Species with Several Delays

利用重合度理论中的延拓定理,研究一类具有任意有限时滞的三种群非自治Lotka-Volteraa互惠系统正周期解的存在性,并运用分析技巧获得了一个有界开集和至少存在一个周期正解的充分条件.结果表明,三种群的互惠系数和密度制约系数在一定条件下,系统将产生生物性周期振荡现象.

Using the continuation theorem based on coincidence degree theory, we studied the existence of positive periodic solutions for a Lotka-Volteraa faeuhative mutualism system of three species with several delays. One bounded open set and a set of sufficient conditions for this system to have at least one positive periodic solution were obtained by using analytic technique. It was revealed that when the faeuhative mutualism coefficient and density dependence coefficient of three species are under certain conditions, the system will bring periodic oscillation of biological nature.