摘要
考虑节能减排量,碳排放量和经济增长量之间的关系,以及时间延迟现象,建立含时间延迟的三维节能减排系统的微分方程模型,分析平衡点及其稳定性态,得到出现Hopf分支的条件.利用中心流形理论和规范性方法给出Hopf分支的性质.数值模拟验证了理论结果的有效性.
This paper focuses on the a three-dimensional energy-saving and emission- reduction evolution system with time delay which typically demonstrates the relationships among the amount of energy-saving and emission-reduction, the amount of carbon emission and the amount of economic growth. The stability properties of the equilibrium points are analyzed and it is found that the Hopf bifurcation appears under some conditions. By using the center manifold theorem and normal form method, we obtain the explicit formulae revealing the properties of the periodic solutions of Hopf bifurcation to show application effects of the system. Numerical simulations illustrate effectiveness of our results.
出处
《数学的实践与认识》
北大核心
2016年第4期269-276,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金项目(61203058)
北方工业大学"人才强校行动计划青年拔尖人才项目(XN131)"
北方工业大学"科研创新团队建设计划项目(XN129)"
实验室建设一公共数学网络教学平台建设(XN041)
关键词
节能减排
时间延迟
平衡点
稳定性
HOPF分支
a three-dimensional energy-saving and emission-reduction system
time delay
equilibrium point
stability
Hopf bifurcation
