The Implications of Optimal Harvesting Strategies for Sustainable Management of Ecosystems

Abstract

This study focuses on investigating the dynamics of prey-predator models and competition within a species, using the Beddington-DeAngelis functional response. Specifically, we can analyze the model's dynamic behavior by varying the harvesting rate as a bifurcation parameter. The system is constrained to the desired state by the harvesting efforts, which are intended to manage the system's cyclical behavior. The existence and stability of the equilibria are analyzed using the characteristic equation and the Jacobian matrix. This study examines the stability of the positive equilibrium and investigates the presence of Hopf bifurcation through analysis of the eigenvalues. Also, the existence of binomic equilibria is derived from the proposed model. The optimal harvesting strategy is determined by applying Pontryagin's maximum principle. The analytical results are supported by numerical simulations that are illustrated