摘要
讨论一类具有Holling-N类功能性反应的离散捕食系统的永久持续生存性和周期解的存在性。首先建立具有Holling-N类功能性反应的食饵-捕食系统的离散化模型,然后应用不等式技巧,获得系统永久持续生存的一个充分条件为:假设(H1):r1Lm>αUM2成立,则m1≤limn→∞infx(n),m2≤nl→im∞infy(n),其中m1=min{(r1Lm-αUM2)/aUm,((r1Lm-αUM2)/aUm)exp(r1L-aU(M1+ε)-αUM/2)}m,m2=min{r2L/bU,r2L/bUexp(r2L-bUM2})。最后利用Brouwer不动点定理,得到系统正周期解的存在性。
Based on the previous studies of functional reaction Holling limited predator-prey system,this paper expands Limited class to N and discusses the permanence and existence of periodic solution for predator-prey system with Holling-N type functional response.Firstly,a discrete model of the system is formulated.Then,by the skills of inequalities,we obtain a sufficient condition ensuring the permanence for predator-prey system.m1≤limn→∞infx（n）,m2≤nl→im∞infy（n）,where m1=min{（r1Lm-αUM2）/aUm,（（r1Lm-αUM2）/aUm）exp（r1L-aU（M1＋ε）-αUM/2）}m,m2=min{r2L/bU,r2L/bUexp（r2L-bUM2}）.Under the assumption of（H1） ,（H1） ： r1Lm αUM2.Finally,based on the results,the existence of periodic solution of system is derived by using Brouwer fixed point theory.
出处
《重庆师范大学学报（自然科学版）》
CAS
2010年第5期33-36,共4页
Journal of Chongqing Normal University:Natural Science
基金
国家自然科学基金(No.10971240
No.10926033
No.10926170)
重庆市自然科学基金(No.CSTC2008BB2364
No.CSTC2009BB2389)
重庆市教委科研项目(No.KJ080806)
