一类双时滞能源价格模型的稳定性及Hopf分支分析

对具有两个时滞的能源价格模型,通过分析线性方程对应的超越特征方程根的分布情况,运用Nyquist准则,研究系统零解的稳定性以及局部Hopf分支的性质,得到平衡点稳定的充分条件及产生Hopf分支的条件;利用规范型理论和中心流形定理讨论系统Hopf分支的分支方向和分支周期解的稳定性,给出关于分支方向和分支周期解稳定性的计算公式。利用MATLAB软件进行相应的数值模拟,通过数值例子验证了理论分析的结果。

Stabilty and Hopf bifurcation analysis in energy price model with two delays

The energy Price Model with two delays is considered.Firstly,the local stability of the zero solution of this system and the property of local Hopf bifurcation are discussed by analyzing the corresponding transcendental characteristic equation of the linearized equation and employing Nyquist criteria,then the sufficient conditions of the stability of the equilibrium solution and appearing Hopf bifurcation are received.Secondly,the explicit formulae for determining the direction of the Hopf bifurcation and the stability of these periodic solutions bifurcating from the steady states are derived by using the normal form method and center manifold theorem.Finally,some numerical simulations are carried out by using MATLAB,and the results are consistent with theoretical analysis results.