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Non-constant Prey Harvesting in a Ratio-Dependent Predator-Prey System with Predator Self Limitation and Prey using a Constant Refuge

Sapna Devi, Rameshwar Prasad Mishra


This paper deals with a ratio-dependent predator-prey model with predator self limitation in which prey species use a constant refuge. Harvesting of only that population of prey
species has been considered which is not using refuge. Conditions for local as well as global stability have been derived. Optimal harvesting policy has been discussed treating
tax as control variable. By numerical simulations it is shown that the dynamic behaviour of the system is very much affected by the prey refuge parameter and the level of tax imposed. It is also shown that the self limitation parameter plays a very crucial role in maintaining the predator population at appropriate level when prey population increases or decreases.


Predator-prey; prey refuge; self limitation; tax; stability; optimal harvesting; numerical simulation.

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