Effects of supplying alternative food in a predator–prey model with harvesting

In this paper, we propose a tritrophic predator–prey model with harvesting where the top-predator population is partially supported with alternative food. We report the consequences of providing alternative food to the top-predator in a top-predator harvested model. The extinction criterion for top-...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 234; pp. 150 - 166
Main Authors Sahoo, Banshidhar, Poria, Swarup
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.05.2014
Subjects
Alternative resource
Bifurcation
Extinction
Foods
Harvesting
Hopf bifurcation
Hopf point
Mathematical models
Maximum principle
Predator–prey
Supplying
Wildlife conservation
Bifurcation
Hopf point
Predator–prey
Extinction
Alternative resource
Harvesting
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Summary:In this paper, we propose a tritrophic predator–prey model with harvesting where the top-predator population is partially supported with alternative food. We report the consequences of providing alternative food to the top-predator in a top-predator harvested model. The extinction criterion for top-predator population, local stability of equilibrium points and persistence conditions are discussed theoretically. Pontryagins maximum principle is used to characterize the optimal control of harvesting. We have derived the condition of Hopf bifurcation by varying harvesting effort. The bifurcation diagrams of the system with respect to harvesting effort in presence of alternative food are given. Our analysis show that alternative food can prevent top-predator extinction risk at higher harvesting effort and plays a vital role for biological conservation of species.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.02.039