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2008, Volume 10, Issue 4: 857-871. Doi: 10.3934/dcdsb.2008.10.857
This issue Previous Article Asymptotic behavior of linearized viscoelastic flow problem Next Article Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems

Global dynamics of a Predator-Prey model with Hassell-Varley Type functional response

  • 1.

    Department of Mathematics, National Tsing Hua University, Hsinchu 300

  • 2.

    Department of Mathematics, National Chung Cheng University, Min-Hsiung, Chia-Yi 621

  • 3.

    Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804

Received:  July 31, 2007
Revised:  January 31, 2008
Published:  August 2008
Abstract Related Papers Cited by
    Abstract
  • Predator-prey models with Hassell-Varley type functional response are appropriate for interactions where predators form groups and have applications in biological control. Here we present a systematic global qualitative analysis to a general predator-prey model with Hassell-Varley type functional response. We show that the predator free equilibrium is a global attractor only when the predator death rate is greater than its growth ability. The positive equilibrium exists if the above relation reverses. In cases of practical interest, we show that the local stability of the positive steady state implies its global stability with respect to positive solutions. For terrestrial predators that form a fixed number of tight groups, we show that the existence of an unstable positive equilibrium in the predator-prey model implies the existence of an unique nontrivial positive limit cycle.
    Mathematics Subject Classification: 34D05, 34D20, 92D25.

    Citation:
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