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A Predator-Prey Model with Crowley-Martin Response for Predation

Nijamuddin Ali, Krishnendu Sarkar, Lakshmi Narayan Guin

Abstract



In this paper, we offer and investigate stability (local and global) and bifurcation (Hopf-Andronov) analyses of a Crowley-Martin predator-prey model system with Qiwu’s growth for prey species and intra-specific competition among predator species. Initially, by virtue of the comparison principle, we achieve boundedness results for both the interacting species. Subsequently, by means of linear stability analysis of the proposed model, we demonstrate that under some parametric restrictions the unique positive equilibrium solution is locally as well as globally stable. Consequently, the direction of Hopf bifurcation and stability of bifurcating periodic solutions are studied. At the end of the investigation, we wind up our findings via intra-specific competition among predator species and present a concise discussion.

Keywords


Interacting species model, Crowle-Martin functional response Intra-specific competition, Stability and bifurcation analyses, Construction of Lyapunov function.

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