Dynamics of optimal harvesting in an Ammensal-Adversarial interaction

Abstract

This article discusses the stability of a two-species ecosystem composed of an ammensal (x) and an adversarial (y) species that are continuously harvested. A mathematical model is defined by a system of two nonlinear ordinary differential equations of first order. The considered system's boundedness is investigated. The local stability of the system is described using a variational matrix, while the global stability is examined using Lyapunov's function. The prerequisite for the system to exist in bionomic equilibrium has been identified. The ideal harvesting technique is determined using the maximal principle proposed by Pontryagin. In MATLAB simulations, the stability of the deterministic system is demonstrated for the specified set of parameters.

Keywords

• Ammensal
• Adversarial
• Local and global stability
• Bionomic equilibrium
• Optimal harvesting