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Effect of Stage Structure in Predator-Prey Model with Crowley-Martin Functional Response

Sumit Kaur Bhatia, Sudipa Chauhan, Apurva Agarwal, Riya Jain

Abstract



In this paper, we study the effect of stage-structure on the dynamics of predator prey system with Crowley-Martin functional response. It is assumed that immature predators cannot catch the prey and their food is given to them by their parents (mature predators). We have obtained boundary and interior equilibrium points of the system. We have also obtained conditions ensuring the local stability of the equilibrium points, by analyzing eigenvalues of associated characteristic equation of linearized system. Permanence of the system has also been obtained.
Numerical simulation are carried out based on four important control parameters: interference among predators, handling time, death rate of mature prey and capturing rate. We have proved that predators gradually decrease and die out as we increase b (interference among predators). Further, when stage structure is considered in both prey and predator population, predator die out faster in comparison with the case when there is no stage structure in predator. We have also proved that the predator population decreases with increase in handling rate and the decrease
in predator population is more in system when stage structure in predator is considered. Based on control parameter, death rate of mature prey, we obtained the result that the prey and predator population will survive for much longer period when there is stage structuring in both prey and predator population, even if we increase the death rate to a large value. Finally, we proved that with the decrease in capturing rate, the predator population increases.

Keywords


Predator-Prey system, Crowley-Martin functional, Stage Structure, stability, Permanence.

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