Homoclinic and heteroclinic chaos in a triple-well oscillator
Homoclinic and heteroclinic chaos in a triple-well oscillator
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DOI：
10.1006/jsvi.1995.0448
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发表时间：
1995-09
影响因子：
4.7
通讯作者：
R. Chacón;J. D. Bejarano
中科院分区：
文献类型：
--
作者：
R. Chacón;J. D. Bejarano
摘要给出了具有三个稳定和两个不稳定平衡位置的非线性振子混沌振动的解析形式的Holmes-Melnikov判据。研究了同宿和异宿分岔的混沌阈值随两个参数的变化：驱动项的频率ω和稳定与不稳定平衡位置之比[公式]。证明了该极限[公式]与两个相关的Duffing型和反Duffing型振子有关。对于一组参数值在该地区的特别感兴趣的，获得良好的协议之间的理论预测和数值计算。此外，作为[公式]，在[公式]-同宿分岔的最混沌频率处观察到持续时间更长的间歇性瞬态运动。
Abstract Holmes-Melnikov criteria for chaotic vibrations of a non-linear oscillator having three stable and two unstable equilibrium positions are obtained in analytic form. The chaotic threshold for homoclinic and heteroclinic bifurcations is studied as a function of two parameters: the frequency ω of the driving term, and the ratio between the stable and unstable equilibrium positions[formula]. It is shown that the limits[formula]connect with two related Duffing and anti-Duffing type oscillators. For a set of parameter values in the region of particular interest, excellent agreement is obtained between the theoretical predictions and numerical calculations. Additionally, as[formula]ever-longer-lasting intermittent transient motion is observed at[formula]—the most chaotic frequency for homoclinic bifurcation.