Periodic solutions and permanence for a delayed nonautonomous ratio-dependent predator-prey model with Holling type functional response

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:162

Article

Wang, LL ; Li, WT

关键词: predator-prey model;    functional response;    positive periodic solution;    coincidence degree;    permanence;   

DOI  :  10.1016/j.cam.2003.06.005

来源: Elsevier

【 摘 要 】

By using the continuation theorem of coincidence degree theory, the existence of positive periodic solutions for a delayed ratio-dependent predator-prey model with Holling type III functional response x'(t) = x(t)[a(t) - b(t) integral(-infinity)(t)(t-s)x(s)ds]- c(t)x(2)(t)y(t)/m(2)y(2)(t) + x(2)(t), y'(t) = y(t) [e(t)x(2)(t-tau)/m(2)y(2)(t-tau)+x(2)(t-tau) - d(t)], is established, where a(t), b(t), c(t), e(t) and d(t) are all positive periodic continuous functions with period omega > 0, m > 0 and k(s) is a measurable function with period omega, tau is a nonnegative constant. The permanence of the system is also considered. In particular, if k(s) = delta(0)(s), where delta(0)(s) is the Dirac delta function at s = 0, our results show that the permanence of the above system is equivalent to the existence of positive periodic solution. (C) 2003 Elsevier B.V. All rights reserved.

【 授权许可】

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