Optimal Harvesting in a Tritrophic Food Chain Model with Ratio-Dependent Functional Response

Abstract

The present paper deals with a non-linear mathematical model of three
species food chain community having ratio-dependent functional response, where
all the species are subjected to optimal harvesting effort with tax as a control instrument
to avoid over exploitation of populations. Mathematical analysis of the
model equations with regard to the boundedness of solutions, existence of interior
equilibrium and their stabilities are carried out. A combined harvesting policy
for prey, middle predator and top predator species is discussed by using Pontryagin’s
Maximum Principle. To verify our mathematical analysis some numerical
simulations are carried out.