Bifurcations of a prey-predator economic model incorporating stagestructure and a constant proportion refuge

摘要

In this paper, a prey-predator economic model incorporating stage-structure and a constant proportion refuge is established. By using the differential-algebraic system theory and bifurcation theory, the dynamic behaviors of the proposed system with zero and positive economic profit are investigated. It shows that the system has two bifurcation phenomena when the economic profit is zero. One is transcritical bifurcation and the other is singular induced bifurcation which indicates the zero economic profit brings rapid expansion of the population in biological explanation. When the economic profit is positive, the system undergoes saddle-node bifurcation at critical value of positive economic profit.