The stability and Hopf bifurcation of the differential-algebraic biological economic system with single harvesting

Abstract

Genecology has developed quickly and systematically by utilizing mathematical principle. The research about the prey-predator system is more and more thorough, closes to the social reality. Considering the actual application, we establish a class of differential-algebraic biological economic systems. And, we study the stability of this system by utilizing the Hopf bifurcation theorem and the new normal form. Here, economic factor m as a bifurcation parameter, it is found that the periodic solution will occur when the parameter m closes to a certain value m0.