PERSISTENCE IN A RATIO-DEPENDENT PREDATOR-PREY-RESOURCE MODEL WITH STAGE STRUCTURE FOR PREY

Abstract

This paper deals with a ratio-dependent predator-prey model where the prey population is stage-structured consisting of immature and mature stages and the predator population is influenced by the resource biomass. By means of a transformation of variables, we transform the model into a dynamical system in such a way that there is one-to-one correspondence between the positive values of the original model and the positive values of the transformed model, so that the results which are true for the transformed model are also true for the original model. Dynamical behaviors such as positivity, boundedness, stability, bifurcation and persistence of the model are studied analytically using theory of differential equations. Computer simulations are carried out to substantiate the analytical findings. It is noted that the influence of the resource biomass on the predator population may lead to the extinction of prey population at a lesser value of maturity time in comparison to the absence of the resource biomass.