Stability and optimal harvesting of a predator-prey system combining prey refuge with fuzzy biological parameters

Abstract

In this manuscript, a novel predator-prey system combining prey refuge with fuzzy parameters is formulated. Sufficient conditions for the existence and stability of biological equilibria are derived. The existence of bionomic equilibria is discussed under fuzzy biological parameters. The optimal harvesting policy, by Pontryagin's maximal principle, is also investigated under imprecise inflation and discount in fuzzy environment. Meticulous numerical simulations are performed to validate our theoretical analysis in detail.

Keywords

• predator-prey system
• prey refuge
• fuzzy number
• stability
• bionomic equilibrium
• fuzzy optimal harvesting