Dynamic behavior of a predator–prey system of combined harvesting with interval-valued rate parameters

Abstract

This paper presents the application of interval number in the modeling of prey–predator interaction. We introduce a biological model referred to as an imprecise prey–predator model. Due to the lack of precise numerical information of the biological parameters such as prey population growth rate, predator population decay rate, and predation coefficients, we consider the model parameters with imprecise data as form of an interval. We consider a prey–predator harvesting model under impreciseness and thereby first time incorporate symmetric parametric functional form of interval to study the various aspects of the model. Further, the biological equilibrium points of the model are identified, and their stabilities are discussed. The existence of bio-economic equilibrium of the model is also discussed under impreciseness. We also study the optimal harvest policy and obtain the solution in the interior equilibrium using Pontryagin’s maximum principle under impreciseness. Finally, examples are provided to support our new approach by numerical and graphical presentation.