The Effect of Prey Refuges on a Three Species Food Chain Model

A refuge model is developed for a resource-based ecosystem. The predator functional responses are taken to be of Holling type I and II, respectively. Stability analyses are carried out for both the cases. Bifurcation phenomenon occurred only for system with Holling type II predator functional response. We identify the parameter which ensures long-term survival of all the populations. The effects of refuges have been established on equilibrium densities of prey and predator population, respectively. The results show that the effects of refuges used by prey increase the equilibrium density of prey population. As far as the predator population is concerned, when prey density at equilibrium level remains below a certain threshold value, increasing the amount of prey refuge can decrease the predator densities. Numerical examples are provided to support our results.