Affiliations: [a] Department of Mathematics, National Institute of Technology, Agartala, Jirania, Tripura, India
| [b] Department of Mathematics & SRM Research Institute, SRM University, Kattankulathur, Tamil Nadu, India
| [c] Department of Mathematics, Midnapore College (Autonomous), Midnapore, West Midnapore, West Bengal, India
Correspondence:
[*]
Corresponding author. Susmita Paul, Department of Mathematics, National Institute of Technology, Agartala,
Jirania-799046, Tripura, India. E-mail: [email protected].
Abstract: Interrelationship between species plays an important role to structure the ecosystem and also controls the dynamics of other species in that ecosystem. Mutualism is the way in which two organisms of different species exist in a relationship where each individual benefits from the activity of the other. In general, in our ecosystem, harvesting is a very frequently used process to exploit biological resources for the welfare of our social and economic purposes. In this article a two species mutualistic harvesting model with imprecise biological parameters has been developed. Due to lack of precise numerical information of the biological parameters such as population growth and cooperation rate, we consider the parameters of the proposed model with imprecise data as the form of interval in nature. After formulation of this imprecise model we discuss the existence of various equilibrium points and their stability. Then we investigate the effect of MSY policy in this mutualistic system, where the model’s population follow logistic law of growth. We,then try to find the existence of bionomic equilibrium in the said imprecise environment. We also try to carry out the equilibrium solution of the control problem which is derived and solved the optimal harvesting policy. All the analytical findings are illustrated through computer simulation which is followed by discussions and conclusions in an elegant way.
Keywords: Mutualism, harvesting, imprecise parameter, local stability, optimal control, Pontryagin’s maximum principle, MSY
