Abstract
In this paper we have discussed about the dynamics of three species (two preys and one predator) delayed predator–prey model with cooperation among the preys against predation. We accept that the rate of change of density of population relies on the growth, death and in addition intra-species competition for the predators. The growth rate for preys is thought to be logistic. Delays are taken just in the growth components for each of the species. With this model we have demonstrated that the system has permanence. Taking the delays as the bifurcation parameter, the stability of the interior equilibrium point has been discussed analytically and numerically. Critical value of the delay is obtained where the Hopf-bifurcation happens. In presence of delay by constructing a Lyapunov function local asymptotic stability of the positive equilibrium point is discussed.
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