Qualitative analysis of a generalist prey-predator model with time delay

Abstract

As we know from theory of evolution in ecology that the generalist predators feed on a variety of prey species may tend to persist in an ecosystem even if one particular prey species is absent in that environment. Predation by generalist predators is followed by a sigmoidal functional responsewhich is ensured in literature. We already knows that a mathematical predator–prey  typemodel with  sigmoidal functional response is found to be more realistic and stable than for a Holling type II functional response. In our model the generalist predator may go to extinct in the absence of one focal prey.It’s dynamics are studied in terms of the local and global aspect and stabilities are verified around the positive equilibrium with the impact of constant delay in the functional response term as some time will be required for gestation of prey for predators. The condition for Hopf-bifurcation of the system has been derived. Numerical computer simulations have been done and compared with the analytical results of the model analysis.