Hopf bifurcation and stability for a differential-algebraic biological economic system

Guodong Zhang, Lulu Zhu, Boshan Chen
2010 Applied Mathematics and Computation  
In this paper, we analyze the stability and Hopf bifurcation of the biological economic system based on the new normal form and the Hopf bifurcation theorem. The basic model we consider is owed to a ratio-dependent predator-prey system with harvesting, compared with other researches on dynamics of predator-prey population, this system is described by differential-algebraic equations due to economic factor. Here l as bifurcation parameter, it is found that periodic solutions arise from stable
more » ... tionary states when the parameter l increases close to a certain limit. Finally, numerical simulations illustrate the effectiveness of our results. Ó
doi:10.1016/j.amc.2010.05.065 fatcat:bnhgpruqcfaejbtbmjzuqf53ue