一类具时滞和比率依赖的捕食-食饵模型2个周期解存在性  

Existence of Two Periodic Solutions for a Generalized Delayed Ratio-dependent Predator-prey Model with Holling Type Ⅲ Functional Response

作　　者：吴书韬 梁峰[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241003

出　　处：《淮北师范大学学报（自然科学版）》2016年第4期15-21,共7页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省自然科学基金项目(1308085MA08)

摘　　要：研究一类带有Holling III型反应函数的捕食-食饵模型{ì?dx(t)t?)[r1(t)-a(t)x(t-τ1(t))-b(t)íd=xt(∫t-∞k(t-s)x(s)d]c-1(t)x(t)y2(ts)m2y2τ(t)+x2(t),?dy(t)d=y2(t))y(t-τt(t)[-r2(t)c+2(t)x(t-))2(t?))m2y2(t-τ2(t+x2(t-τ2(t))].运用重合度拓展定理,证明其存在2个正周期解.并举一个实例验证结论的可行性.In this paper,the authors studies the existence of two periodic solutions for a generalizeddelayed ratio-dependent predator-prey model with Holling type III functional response:ìxc?d(t)- at- s?(t)x(t- τ1(t))- b(t))x(s)ds]-1(t)x(t)y2(t)m2y2+ x2íd= xt(t)[r1(t)∫t-∞k((t)(t)??dy(t)?d= y.t(t)[-r2(t)c+22(t)x(t- τ2(t))y(t- τ2(t))my2(t- τ2(t))+ x2(t- τ2(t))]By applying Mawhin′s continuation theorem,some new results on the existence of two positive periodic solu-tions are obtained.An example is represented to illustrate the feasibility of our main result.

关 键 词：周期解 Mawhin重合度拓展定理 时滞 捕食-食饵模型 比率依赖 

分 类 号：O175[理学—数学]