一类具有庇护效应的非自治的生物捕食模型

A Non-autonomous Predator-prey Model with Refuge Effect

庇护效应广泛的存在于捕食模型中,被捕食者为寻求自身的生存采取"庇护"的方式,是一种合理的自然现象.将庇护效应引入到捕食模型能更贴切地模拟实际环境中的生物种群关系.该文研究了一类具有庇护效应的非自治生物捕食模型的周期解,选取指标为0的Fredholm映射L,以及■上的L-紧的算子N,同时估计其先验界,构造X上的有界开子集Ω,利用Mawhin重合度理论中的连续性定理,得到该模型存在周期解的充分条件.

As refuge effect widely exists in the predator model,it is a very reasonable natural phenomenon for the prey to take refuge in order to seek its own survival.Therefore,the dynamics of a predatorprey model with refuge effect seems to be more realistic if the different growth rate for the prey populations in refuge region and predatory region are considered respectively.Thus,a Fredholm map L with index 0 and the L-compact operator N on■are selected and their prior bounds are estimated in this paper.By constructing a bounded open subsetΩon X and using the continuity theorem in Mawhin coincidence theory,sufficient conditions for the existence of periodic solutions in the model are obtained.