Dynamical study of the theta-logistic predator-prey model incorporating gregarious behavior of prey

Abstract

Relation between species and their livelihood environment in ecological systems is very complex. For that reason, in order to study predator-prey relations, modeling is essential in biomathematics. The vital components of predator-prey models are prey species' growth function in the absence of a predator and the functional response. In this article, we proposed a predator-prey model with gregarious prey. In the existing literature, square-root functional response incorporates the gregarious behavior of prey. This study considers the generalized square root functional response and theta-logistic growth of prey in the absence of a predator. The effect of functional response parameters on stability, limit cycle, and Hopf bifurcation on the proposed model has been discussed. Numerical analysis is performed on the basis of some hypothetical parameter values to analyze the model numerically.

Keywords

• predator-prey
• functional response
• limit cycle
• stability
• hopf bifurcation.