Effect of a functional response-dependent prey refuge in a predator–prey model

• A general prey refuge predator–prey Model proposed.
• Influence of predator intra-specific competition is established in prey refuge model.
• Complexity in the prey refuge model.
• Role of functional response is established in prey refuge model.

We propose two mathematical models for predator–prey interactions allowing for prey refuge. The novelty lies in the assumption that the amount of prey in refugia is proportional not only to the encounters between prey and predator, but also it is modelled by a Holling type II response function. The second model also accounts for predator's intraspecific competition. We fully analyse the models and discuss all possible coexistence equilibria configurations and their local and global stability. A saddle-node bifurcation analysis is also performed for a wide set of parameter ranges. The ultimate behavior of the systems depends mainly on two relevant parameters, the prey refuge constant and the predator's intraspecific competition.