基于比率的两种群捕食者-食饵系统的周期解

对于捕食者 食饵系统已有大量的研究工作,主要集中于解的稳定性、持久性等,关于周期性结论很少。本文研究了一类非自治的具有时滞和基于比率且有Machaelis Menten型功能性反应的两种群捕食者 食饵周期系统 x1=x1(t)(a(t)-b(t)x1(t)-c(t)x1(t)x2(t)m(t)x22(t)+x21(t)), x2=x2(t)(-d(t)+e(t)x21(t-τ)m(t)x22(t-τ)+x21(t-τ)),利用Mawhin的重合度理论和不等式技巧,找到了系统的1个先验界,并建立了这类系统正周期解的存在性判据。

Periodic Solutions of a Ratio-dependent Predator-prey System of Tow Species

For the predator-prey most work of study focuses on the stability and persistence while there have ever been little results about the periodicity.In this paper,we study a two-species ratio-dependent predator-prey system with time delay and Machaelis-menten type functional response _1=x_1(t)(a(t)-b(t)x_1(t)-c(t)x_1(t)x_2(t)m(t)x~2_2(t) x~2_1(t)), x_2=x_2(t)(-d(t) e(t)x~2_1(t-r)m(t)x~2_2(t-r) x~2_1(t-r)). By using Mawhin's coincidence degree thoery and technique of inequalities,we obtain a prior boundary of the system,and establish the existence result of positive periodic solution for the system.