Stability and Bionomic Analysis of Fuzzy Prey–Predator Harvesting Model in Presence of Toxicity: A Dynamic Approach

Abstract

This paper deals with a prey-predator model in which both the species are infected by some toxicants which are released by some other species or source with fuzzy biological parameters. The application of fuzzy differential equation in the modeling of prey-predator populations with the effect of toxicants is presented. The dynamical behavior and harvesting of the fuzzy exploited system are studied by using the utility function method. Sufficient conditions for the local stability of the positive equilibrium are obtained by analyzing the characteristic equation. Furthermore, the possibility of the existence of bionomic equilibrium is studied under imprecise biological parameters. The study of the presence of toxic substance and harvesting in the modeling system can have significant impact on the existence of both the species, which is in line with reality. Numerical simulation results are presented to validate the theoretical analysis.