Parameter uncertainty in biomathematical model described by one-prey two-predator system with mutualism

Abstract

In this paper, a three-species system consisting of two predators which are in mutualism with each other and preying on the same single prey is considered. Also, the prey and first predator are harvested under optimal conditions. The values of the biological parameters depend on the collection of data from the experts as well as on the nature of the environment in which prey–predator system are considered. So the biological parameters are not precise in reality. This paper presents a different approach to study the prey–predator model with imprecise biological parameters. All the possible equilibrium points are identified and the local as well as global stability criteria under impreciseness are discussed. The possibility of existence of bionomic equilibrium is discussed. The optimal harvesting policy is studied using Pontryagin’s maximum principle. Numerical examples are provided to support the proposed approach.