中文摘要：

考虑三维节能减排系统，施加时滞反馈控制，建立反馈控制下的节能减排系统，求解平衡点，分析系统稳定性，得到出现Hopf分支的条件．利用中心流形定理和Poincare规范型方法讨论Hopf分支的性质．给定参数进行数值模拟，验证理论结果的有效性．

英文摘要：

This paper considers a three-dimensional energy saving and emission reduction system. A delayed feedback controller is proposed to stabilize the system which was originally unstable. The stability properties of the equilibrium points are analyzed and the Hopf bifurcation appears under some conditions. By using the center manifold theorem and normal form method, the explicit formulae axe obtained revealing the properties of the periodic solutions of Hopf bifurcation to show stabilizing effects of the delayed feedback controller. Numerical simulations illustrate effectiveness of our results.