时滞变量对能源结构模型稳定性的影响

Research on the Influence of Delay on the Stability of Energy Structure Model

在原有能源结构模型的基础上,考虑环境污染对煤炭消耗影响的延迟性,以及煤炭收益对油气消费量影响的滞后性,构建了一种带双时滞的能源结构模型。使用非线性动力学理论和复杂系统理论,研究了时滞参数的变化对系统稳定性的影响。首先,判断两种情况下Hopf分岔的存在性;其次,研究参数组合的变化对系统稳定性的影响;最后,通过数值模拟,借助功率谱、三维立体图和四维立体图等工具,对研究结论进行了验证。研究表明,时滞变量的过度增大,将导致能源结构模型失去稳定性,不利于政府调整能源结构和制定能源政策。

Based on the original energy structure model, taking the delay into account, the energy structure model with two delays is established. In this paper, the influence of time delay parameter on the stability of the system is studied by using nonlinear dynamics theory and complex system theory. First, the existence of Hopf bifurcation is determined under two kinds of situations;secondly,the influence of the changes of the parameter combinations on the stability of the system is studied. Finally, the correct- ness of the conclusion is verified by means of power spectrum, 3-D graph and 4-D graph. The research shows that the excessive increase of time delay variables will lead to the loss of stability of the energy structure model,which is not conducive for the government to adjust the energy structure and to develop the energy policy.