捕食者具有阶段结构和基于比率捕食系统的定性分析

Qualitative Analysis in a Ratio-Based Predator-Prey System with Stage Structure for Predator

研究了一类捕食者具有阶段结构和基于比率捕食系统的解的性态,通过应用比较原理和分析方法获得了当-τ≤θ<0时,若x(θ),y(θ)≥0,x(0),y(0)>0,则系统的解在t≥0时是正的;若αre-rτ>av时,系统的任意正解是有界的;若r>b/m且αe-rτr-m/b/a>v,则系统是持久的。最后通过数值模拟阐述了所得结论的正确性。

In this paper, a predator-prey system in a ratio-based predator with state-structure for predator is investigated. By using methods of the comparison principle and analysis, some sufficient conditions are obtained if -τ≤θ〈0, x（θ）,y（θ）≥0,x（0）,y（0）〉0, and then the solution of the system is positive for t≥0;If αre-rτ〉av, and then any positive solutions of system is bound-ed; and if r〉b/m and αe-rτr-m/b/a〉v, then system is persistent. Finally, numerical simulation describes the conclusions are correct.