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Abstract: In this paper, we consider a differential–algebraic biological economic system with time delay and harvesting where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the differential–algebraic biological economic system based on the normal form approach and the center manifold theory. At last, numerical simulations are performed to illustrate the analytical results. [Copyright &y& Elsevier]

Abstract: 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 μ as bifurcation parameter, it is found that periodic solutions arise from stable stationary states when the parameter μ increases close to a certain limit. Finally, numerical simulations illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]