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从确定性到随机性:用基于控制的延续方法提取杂的双位振荡器的分支图的极限
Henrik T Sykora1, Sandor Beregi2
1Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary.
概括
基于控制的延续 (CBC) 有效地估计了杂的非线性系统中的分叉图. 这种方法提供了可靠的振幅近似近周期性解决方案在实验中适度噪声.
科学领域:
- 非线性动力学和控制控制
- 动态系统的实验性表征
- 工程中的随机过程 工程中的随机过程
背景情况:
- 噪音严重阻碍了从动态系统中提取信息,特别是那些具有共存状态的系统.
- 基于控制的延续 (CBC) 是一种标准的确定性方法,用于实验性地描述非线性系统.
- 现实世界的实验涉及固有的噪音,对CBC等确定性分析方法构成挑战.
研究的目的:
- 调查基于控制的延续 (CBC) 在从固有噪音的实验数据中提取信息的能力.
- 评估添加噪声对非线性系统的分支图的影响.
- 评估CBC在对噪声系统的表征方面的表现,与已知的确定性模型相比.
主要方法:
- 研究了Hopf正常形式与五进制项和附加噪声.
- 采用基于步行矩阵乘法的路径积分 (SMM-PI) 方法,在不同噪声强度下近似计算稳定状态概率密度函数 (PDF).
- 关联PDF的局部极端与极限周期,并将结果的分叉图与CBC估计进行了比较.
主要成果:
- 基于控制的延续 (CBC) 准确地估计了噪音系统的分叉图,用于小到中等噪音强度.
- SMM-PI方法成功地接近了不同噪声水平的稳定状态PDF.
- 在杂的实验中,CBC衍生的振幅作为近周期性溶液振动振幅的可靠"最佳猜测"代理.
结论:
- 基于控制的延续 (CBC) 对于表征非线性系统而言是强大而有效的,即使存在显著的实验噪声.
- 这项研究验证了CBC在实际,杂的实验环境中对近似关键动态特征 (如振动振幅) 的实用性.
- 研究结果表明,CBC可以自信地应用于涉及杂非线性动态系统的广泛实验.
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