Stability Analysis of a Non-linear Harvesting Model with Taxation

Abstract

This paper formulates and analyzes a non-linear harvesting of prey, considered in a prey-predator system. Here, the effort is taken as a dynamic variable. Mathematical analysis of the model system includes the existence, uniqueness and uniform boundedness of the solutions in the positive octant. Authoritarian agency has power over exploitation by striking a tax per unit biomass of the prey species. The conditions for the existence of the positive steady states of the model system are derived. Also the local and global stabilities of several equilibrium points are studied using the Routh Hurwitz criteria and Lyapunov function respectively. Numerical simulations are performed by making use of MATLAB to justify the analytical conclusions.