Simulation of Optimal Harvesting of Three Species Ecological Model with Closed Interval of Biological Parameter Using by Liapunov Function

Abstract

The paper presents the study of three species ecological model with Prey N₁, predator N₂ and competitor to the Predator N₃ and neutral with the predator N₂ with imprecise biological parameters. The model is characterized by a set of first order nonlinear ordinary differential equations. 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 with imprecise data as form of an interval in nature. Many authors have studied prey–predator harvesting model in different form, here we consider a simple prey–predator model under impreciseness and introduce parametric functional form of an interval and then study the model. Equilibrium points of the model are identified, the local stability is discussed using Routh - Hurwitz criteria and global stability by Liapunov function. The existence of bionomic equilibrium of the system has been discussed and optimal harvesting policy is given using Pontryagin’s maximum principle. The stability analysis is supported by Numerical simulation using Mat lab.

Keywords: Prey; Predator; Competitor to the predator; Equilibrium points; interval number, Stability of the equilibrium points; Bionomic Equilibrium; Optimal harvesting policy; Pontryagin’s maximum principle; Numerical simulation using mat lab.

DOI: 10.7176/IEL/9-1-04