### All Issues

Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
 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.