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Volume 5, Number 1, 2015, Pages 28-37                                                                DOI:10.11948/2015003
Global stability of a delayed ratio-dependent predator-prey model with Gompertz growth for prey
Shihua Zhang,Rui Xu
Keywords:Predator-prey model, ratio-dependence, Gompertz growth, stability, bifurcation.
Abstract:
      A delayed ratio-dependent predator-prey model with Gompertz growth for prey is investigated. The local stability of a predator-extinction equilibrium and a coexistence equilibrium is discussed. Furthermore, the existence of Hopf bifurcation at the coexistence equilibrium is established. By constructing a Lyapunov functional, sufficient conditions are obtained for the global stability of the coexistence equilibrium.
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