Permanence of periodic Holling type-IV predator-prey system with stage structure for prey

  • Authors:

  • Wensheng Yang;Xuepeng Li;Zijun Bai

  • Affiliations:

  • School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, PR China;School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, PR China;School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, PR China

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2008

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Abstract

In this paper, we study the permanence of the following periodic Holling type-IV predator-prey system with stage structure for prey x@?"1(t)=a(t)x"2(t)-b(t)x"1(t)-d(t)x"1^2(t)-p(t)x"1(t)k(t)+x"1^2(t)y(t),x@?"2(t)=c(t)x"1(t)-f(t)x"2^2(t),y@?(t)=y(t)(-g(t)+h(t)x"1(t)k(t)+x"1^2(t)-q(t)y(t)). Under certain assumptions, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.