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Stability and Hopf Bifurcation in a Delayed Predator-Prey System with Herd Behavior

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  • Chaoqun Xu
  • Sanling Yuan

Abstract

A special predator-prey system is investigated in which the prey population exhibits herd behavior in order to provide a self-defense against predators, while the predator is intermediate and its population shows individualistic behavior. Considering the fact that there always exists a time delay in the conversion of the biomass of prey to that of predator in this system, we obtain a delayed predator-prey model with square root functional response and quadratic mortality. For this model, we mainly investigate the stability of positive equilibrium and the existence of Hopf bifurcation by choosing the time delay as a bifurcation parameter.

Suggested Citation

  • Chaoqun Xu & Sanling Yuan, 2014. "Stability and Hopf Bifurcation in a Delayed Predator-Prey System with Herd Behavior," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, April.
    • Handle: RePEc:hin:jnlaaa:568943
    DOI: 10.1155/2014/568943
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