周期演化域上三种群互惠模型的动力学

Dynamics of Three-Species Cooperating Model on Periodically Evolving Domain

通过研究周期演化区域上一类三种群互惠模型,讨论区域的周期演化对种群持续和灭绝的影响.利用上下解方法、比较原理、拟单增系统理论及抛物方程的先验估计理论,研究模型正周期解的存在性及稳定性问题.记ρ为区域演化速率,ρ^(-2)=1 T∫T 01ρ2(t)d t.结果表明:当ρ^(-2)>1时,区域周期演化对互惠种群持续性的影响是消极的;当ρ^(-2)<1时,区域周期演化对互惠种群持续性的影响是积极的;当ρ^(-2)=1时,区域周期演化对互惠种群持续性没有影响.

By studying a class of three-species cooperating models on periodically evolving domain,we discussed the effect of periodic evolution of domain on the persistence and extinction of species.The existence and stability of the positive periodic solution of the model were studied by using the upper and lower solutions method,the comparison principle,the theory of quasi-monotone system and the priori estimates of parabolic equations.We recordedρas the domain evolution rate andρ^(-2)=1 T∫T 01ρ2(t)d t.The results show that the effect of periodically evolving domain on the persistence of species is negative whenρ^(-2)>1,it is positive whenρ^(-2)<1,and there is no effect whenρ^(-2)=1.