Stabilization and de-stabilization of predator-prey systems under harvesting and nutrient enrichment

Abstract

A predator-prey system is modelled by a pair of ordinary differential equations, and the qualitative effects of prey nutrient enrichment and predator harvesting on the stability of the system are studied. Some theoretical analysis concerning the existence of equilibrium points and limit cycles is included. Three models are examined as examples and the concept of practical stability is introduced. For one of the models, computer simulations are included to illustrate the changes in qualitative behaviour under nutrient enrichment and harvesting. The results indicate that care must be taken in harvesting to prevent extinction of the predator and a resulting collapse of the entire ecosystem. This study should, therefore, prove to be a useful tool in resource management and control.