›› 2014, Vol. 53 ›› Issue (5): 66-72.

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Qualitative Analysis for a Predator-prey System with Crowley-Martin Type Functional Response

LI Haixia1,2,LI Yanling1   

  1. 1.College of Mathematics and Information Science, Shaanxi Normal University, Xi-an 710062, China;
    2. Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, China
  • Received:2013-11-29 Online:2014-09-25 Published:2014-09-25

Abstract: The existence and permanence of the positive solutions for a one-prey and two-predators model with Crowley-Martin type functional response are considered. First, the bifurcation from a double eigenvalue for system is discussed by virtue of the space decomposition and the implicit function theorem, and the sufficient conditions for the existence of the positive steady-state solutions are obtained. Moreover, the sufficient conditions for the non-existence of the positive steady-state solutions are given. Finally, asymptotic behavior of the positive solutions of the parabolic system is investigated, and the sufficient conditions for extinction and permanence of the parabolic system are given by using the comparison theorem.

Key words: predator-prey model, Crowley-Martin functional response, bifurcation, the implicit functional theorem, permanence

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