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A delayed predator-prey model with prey population guided anti-predator behaviour and stage structure
Lingshu Wang
Keywords:predator-prey model, anti-predator behaviour, stage structure, time delay, Hopf bifurcation, stability.
Abstract:
      We consider a predator-prey model with stage structure for the prey and anti-predator behaviour such that the adult prey can attack vulnerable predators. In which a time delay due to the gestation of the predator is incorporated into this model. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the positive equilibrium are established, respectively. By using Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are obtained for the global stability of the trivial equilibrium, the predator-extinction equilibrium and the positive equilibrium, respectively. Numerical simulations are performed to illustrate the theoretical results. \ {\bf Key words-- }predator-prey model, anti-predator behaviour, stage structure, time delay, Hopf bifurcation, stability.