The present paper describes a model of resource biomass and population with a non-linear catch rate function on resource biomass. The harvesting effort is assumed to be a dynamical variable. Tax on per unit harvested resource biomass is used as a tool to control exploitation of the resource. Pontryagin’s Maximum Principle is used to find the optimal control to maintain the resource biomass and population at an optimal level. A numerical simulation is also carried out to support the analytical results.
Dubey, B.; Patra, Atasi; and Sahani, S. K.
Modelling the Dynamics of a Renewable Resource under Harvesting with Taxation as a Control Variable,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 9,
2, Article 10.
Available at: https://digitalcommons.pvamu.edu/aam/vol9/iss2/10