BIFURCATION AND CONTROL IN A DIFFERENTIAL-ALGEBRAIC HARVESTED PREY-PREDATOR MODEL WITH STAGE STRUCTURE FOR PREDATOR

Abstract

A differential-algebraic model system which considers a prey-predator system with stage structure for a predator and a harvest effort on the mature predator is proposed. By using the differential-algebraic system and bifurcation theories, the local stability and instability mechanism of the proposed model system are investigated. With the purpose of stabilizing the proposed model system at the positive equilibrium, a state feedback controller is designed. Finally, a numerical simulation is carried out to show the consistency with theoretical analysis and illustrate the effectiveness of the proposed controller.