Discrete System Insights of Logistic Quota Harvesting Model: A Fuzzy Difference Equation Approach

Abstract

Optimal harvesting modeling is a matter of great importance for the sustainability of the eco-system. It is customary to consider the population dynamics in a continuous frame of time. In this paper, a discrete analogue of the study of the Logistic quota harvesting model under uncertainty is developed. The corresponding mathematical model is discussed in terms of nonlinear fuzzy difference equation. Different possible combinations of the fuzzy initial conditions and fuzzy coefficients are used for the manifestation of the difference equation. The equilibrium points and the subsequent stability analysis are carried out with the help of the characterization theorem which converts the fuzzy difference equation to a system of crisp difference equations. The numerical and graphical simulation are practiced to make a clear insight advocated by this study.