A bioeconomic modeling of two-prey and one-predator fishery model with optimal harvesting policy through hybridization approach

Abstract

This paper introduces an imprecise prey–predator model by using interval and fuzzy number in modeling of prey and predator interaction. In a prey–predator system, values of the biological parameter are based on the collection of data by the experts from nature; therefore we consider them as interval numbers. The proposed prey–predator model is consisting of two species which are not only affected by the harvesting of the species but also by the present of predator species. All possible existence of the biological and bionomic equilibrium points of the model are discussed under impreciseness. We derive the conditions for local and global stability. The optimal harvesting policy is studied by considering instantaneous annual rate of discount under fuzziness. By logically hybridizing the interval and fuzzy number methodologies, we find the optimal equilibrium points and harvesting efforts in the form of interval. Finally, numerical examples are illustrated to support the proposed approach.