Stability and Hopf Bifurcation of Delayed Predator-Prey System Incorporating Harvesting

Stability and Hopf Bifurcation of Delayed Predator-Prey System Incorporating Harvesting

A kind of delayed predator-prey system with harvesting is considered in this paper. The influence of harvesting and delay is investigated. Our results show that Hopf bifurcations occur as the delay τ passes through critical values. By using of normal form theory and center manifold theorem, the dire...

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Veröffentlicht in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.175-186-1019
Hauptverfasser: Wei, Fengying, Fang, Yuzhi, Wu, Lanqi
Format: Artikel
Sprache:eng
Schlagworte:
Bifurcation theory
Computer simulation
Delay
Equilibrium
Externality
Harvesting
Hopf bifurcation
Manifolds
Mathematical models
Predation
Stability
Wolves
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Zusammenfassung:A kind of delayed predator-prey system with harvesting is considered in this paper. The influence of harvesting and delay is investigated. Our results show that Hopf bifurcations occur as the delay τ passes through critical values. By using of normal form theory and center manifold theorem, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are obtained. Finally, numerical simulations are given to support our theoretical predictions.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/624162