Pseudo-oscillator Analysis of Scalar Nonlinear Time-Delay Systems Near a Hopf bifurcation
Pseudo-oscillator Analysis of Scalar Nonlinear Time-Delay Systems Near a Hopf bifurcation
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DOI：
10.1142/s0218127407018786
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发表时间：
2007-08
期刊：
影响因子：
--
通讯作者：
Zaihua Wang;Haiyan Hu
中科院分区：
文献类型：
--
作者：
Zaihua Wang;Haiyan Hu
本文提出了一种新的方法--伪振子分析法，研究了一类标量非线性时滞动力系统的Hopf分支附近的局部动力学行为。为此，首先构造了一个伪振子，它是由一个无阻尼振子微扰而成的，其基频与分岔点处的频率相同，且扰动与原系统相关联.接着，伪功率函数，定义为伪振荡器的功率函数，沿着谐波函数被估计沿着。然后，我们得出结论，可以证明的平均伪幂函数的变化的Hopf分岔附近的局部动力学。新方法具有物理直观性强、计算简便的特点，并对Hopf分支所产生的周期解给出了非常精确的预测，三个算例表明了新方法的有效性.
In this paper, a novel method named pseudo-oscillator analysis is developed for the local dynamics near a Hopf bifurcation of scalar nonlinear dynamical systems with time delays. For this purpose, a pseudo-oscillator that is slightly perturbed from an undamped oscillator is firstly constructed, its fundamental frequency is the same as the frequency at the bifurcation point, and the disturbance is associated with the original system. Next, the pseudo-power function, defined as the power function of the pseudo-oscillator, is estimated along a harmonic function. Then we conclude that the local dynamics near the Hopf bifurcation can be justified from the variation of the averaged pseudo-power function. The new method features a clear physical intuition and easy computation, and it yields very accurate prediction for the periodic solution resulted from the Hopf bifurcation, as shown in three illustrative examples.