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Dynamics of an Exploited Prey Predator Model Induced by Sigmoidal Functional Response in Strong Allee Effect

Samadyuti Haldar, Kunal Das, T.K. Kar

Abstract



This work deals with a prey-predator system with an Allee effect induced by two advanced functional response viz. sigmoidal and modified Leslie-Gower for predation and outlay respectively. Here both the communities are harvested by the combined harvesting effort . Initially, we examined some basic properties like the positivity, boundedness, persistence and permanence of the system to validate the system in order to ensconce the long term survival of the species. It is observed that the system is asymptotically stable around some steady states under certain conditions and globally stable. Also the growth rate of prey should be restricted otherwise the system will be unstable through bifurcation. Taking (harvesting effort) as control parameter, we have determine optimal harvesting policy. We have examine the Allee effects (L) leading to investigate about the sustainability of the system. Investigation reveals that the gradual increment of Allee lead the system unstable from a stable state and after a certain threshold level of L, the system may be ruined. Finally, the MSY analysis explores some new findings leading to obtain sustainable maximum yield.

Keywords


Prey-predator model, Sigmoidal functional response, Allee effect, Persistence, Bifurcation, Harvesting, MSY.

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