Effects of fuzzy harvesting on logistic growth models for uncertain ecological parameter

Abstract

This paper presents the effects of two well known harvesting models namely quota harvesting and proportional harvesting on the logistic growth model under fuzziness. In many real life situations it is not possible to have a single growth rate of a species throughout the specified time span. Species are enhanced at different growth rates during their life span that arises due to nature of the soil, whether condition, rain fall, food supply etc. Similarly the total harvesting quantity for quota harvesting model and the proportion of the harvesting quantity for proportional harvesting quantity depend on the nature (need) of the harvester. So these are imprecise in nature, here we assume that the growth rate, constant harvesting quantity and proportion of harvesting quantity are uncertain in reality by considering imprecise by triangular fuzzy number. We find the equilibrium points, bifurcation value and discuss the stability of the equilibrium points of the models under fuzziness with different perspectives. Numerical examples are given to illustrate the harvesting models under fuzziness. Finally graphical illustrations are given to study the effects of harvesting on the logistic growth model under fuzziness.