Sustainable and catastrophic harvest methods in a logistic equation-based growth model of natural resources

Abstract

An analysis of a simple mathematical harvest model of a growing resource, based on the logistic equation, is presented. It is found that selective harvesting on areas with high density of resources is sustainable. On the other hand, a catastrophic loss in the resource density at steady state happens when the harvesting is unselective. Unselective harvesting involves high rates of harvests even for areas with moderate resource density. The latter are used to explain the sudden (irreversible) loss in the natural resources as a result of its abusive utilization.