一类具有阶段结构的食饵-捕食收获模型分析

在2种群相互作用的Lotka-Volterra模型的基础上将捕食者种群分为幼年捕食者和成年捕食者.设幼年捕食者不具有捕食能力而靠其父母来喂养,且幼年捕食者的成熟率与其摄取的营养有关,对成年捕食者以常数收获率进行收获.建立了一类具有阶段结构的食饵-捕食收获模型,利用Hurwitz判别法得到了系统的正平衡点的稳定性随对成年捕食者的收获率和营养对幼年捕食者的影响而变化.

Analysis of a Prey-predator Model under Constant-rate Predator Harvesting with Stage Structure

Based on the two species-interactive Lotka-Volterra model,this paper puts forward a prey-predator model in which predators are split into immature predators and mature predators.It is assumed that immature predators are raised by their parents in the sense that they cannot catch the prey and their foods are provided by parents.Furthermore,it is assumed that the maturation rate of immature predators is a function of the nutrient availability for one immature individual,and mature predators are harvested under constant rate.Based on the assumptions above,this paper formulates a prey-predator model under constant-rate predator harvesting with stage structure.By the Routh-Hurwitz criteria,it is shown that two stability switches of positive equilibrium may occur due to the transition rate incorporating the influence of nutrient,and the harvesting rate to the predator.