Food chain model with logistic growth and selective optimal harvesting under fuzzy environment

Abstract

A multispecies food chain harvesting model is formulated based on Lotka-Voltera model with three species which are affected not only by harvesting but also by the presence of prey, predator and the super predator. In order to understand the dynamics of the system, it is assumed that the all three species follows the logistic law of growth. Further, there is demand for prey predator species in the market and hence selective harvesting of two species is performed. We derive the condition for global stability of the system using a suitable Lyapunov function. The possibility of existence of bioeconomic equilibrium is discussed. The optimal harvest policy is studied and the solution is derived under imprecise inflation in fuzzy environment using Pontryagin’s maximal principle. Finally some numerical examples are discussed to illustrate the model.