Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations

IF 1.2 Q2 MATHEMATICS, APPLIED
Rong Haiwu, W. Xiang-dong, Lu Qizhi, Xu Wei, Fang Tong
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引用次数: 1

Abstract

The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.
谐波和有界噪声激励下非线性振动冲击振荡器安全池的分岔与混沌
研究了在谐波噪声和有界随机噪声作用下,非线性振动冲击振荡器的安全盆侵蚀和混沌运动。利用Melnikov方法计算系统的Melnikov积分,得到混沌运动的参数阈值。利用蒙特卡罗法和龙格-库塔法对安全盆地的侵蚀进行了讨论。当系统的分岔参数经过一个临界值时,随机安全池的特性发生突变,可以定义为一个可选的随机分岔。发现随机噪声会破坏安全池的完整性,使随机分岔的发生提前,使运动的参数阈值在更大的区域内变化,从而使系统变得更加不安全,更容易发生混沌运动。
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来源期刊
Journal of Applied Mathematics
Journal of Applied Mathematics MATHEMATICS, APPLIED-
CiteScore
2.70
自引率
0.00%
发文量
58
审稿时长
3.2 months
期刊介绍: Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics.
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