Habitat complexity of a discrete predator-prey model with Hassell-Varley type functional response

Abstract

Prey-predator models with a refuge effect are particularly significant in ecology. The two common conceptions of refuge in the literature are continual refuge and refuge pro-portionate to prey. Academics are already paying attention to new types of refuge concepts. Prey-predator interaction has become a prominent issue in recent biomathe-matical studies due to its environmental influence. In this paper, the habitat complexity of a predator-prey model with Hassell-Varley type functional response is considered. For this, we focused our study on the question of existence and uniqueness in Sec. 2. And Sec. 3 is devoted to show a generalized stability. Note that this representation also al-lows us to generalize the results obtained recently in the literature. In Sec. 4, we have studied the numerical algorithm for the suggested problem. The paper is ended by two examples illustrating our results.