Bifurcations and feedback control of a stage-structure exploited prey-predator system

Abstract

The present paper describes a bioeconomic modelling of a stage-structure prey-predator system with differential algebraic equations. The criterion for coexistence of the equilibrium points and their stability nature are investigated. Singularity induced bifurcation are studied for zero economic profit and in this perspective, feedback control is designed to preserve the persistence property of the system. In contrast to zero profit, an interior equilibrium point remains stable for positive economic profit. The reasons behind the different nature of the interior equilibriums for zero and positive profit are discussed in conclusion section. Some numerical simulations are given to verify the analytical results. How the maximum profit hampers the system is provided through saddle-node bifurcation in the last subsection of numerical simulation.

International Journal of Engineering, Science and Technology, Vol. 2, No. 6, 2010, pp. 131-141