具有密度依赖扩散的n个捕食与被捕食种群模型的动力学

DYNAMICS OF PREDATOR-PREY N-SPECIES MODELS WITH DENSITY DEPENDENT DIFFUSION

本文研究了在有界闭区域上一类包含n个物种的捕食被捕食模型,其中含有1个被捕食者,n-1个捕食者,而n-1个捕食者之间可能为合作关系或竞争关系.在这个模型中,扩散是密度依赖的,反应函数包含比率依赖.我们得到了一些简单的条件,保证了时间依赖解及相应的稳态问题的正解和拟解的存在性以及解的动力学行为,从而得到了捕食与被捕食物种的共存性.

This paper is concerned with two classes of n-species predator-prey models in a bounded domain which include n- 1 cooperative predators and n - 1 competitive predators. In these models, the diffusion coefficients may be density dependent, and the reaction functions include ratio-dependent. Some simple conditions are obtained to ensure the dynamical behavior of the time-dependent solution in relation to some positive solutions or quasi-solutions of the steady-state problem, which include the existence of these solutions. This dynamical behavior leads to the coexistence of the predator-prey system.