Switching effect of predation on a small size prey species living in two different habitats

A Mathematical model with one prey species living in two different habitats and a predator where the predatory rate diminishes at low population densi ty of prey is investigated. Two habitats are separated by a barrier and pre y species is able to disperse among two different habitats at some cost of the population. The stability analysis is carried out for non-zero equilibr ium values. Using rate of conversion of the prey to predator as bifurcation parameter, the necessary and sufficient condition for a Hopf bifurcation t o occur are derived. It is shown numerically that predation rate does not a lways have stabilizing effect for the prey-predator system.