Chaotic Phenomena and Their Engineering Relevance

混沌现象及其工程相关性

• 批准号: 03044084
• 负责人: UEDA Yoshisuke
• 金额: $ 1.28万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for international Scientific Research
• 财政年份: 1991
• 资助国家: 日本
• 起止时间: 1991 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03044084/
• 关键词: Dynamical systems; Power generation; Fractal basin boundary; Straddle orbit method; Chaotic transients; Bifurcations with indeterminate outcome; Capsize of ships; Ship stabilization mechanism

The study of ordinary differential equations representing the dynamics of two coupled swings has been pursued using digital simulations and algorithms based on the geometrical theory of dynamical systems. These equations were derived from a simple model of dynamical stability of a simple electric power generation system involving two generators connected by a transmission line. Although this system has no chaotic attractors, there is a fractal basin boundary which is of fundamental relevance in determining the engineering stability properties. Substantial progress has been made in understanding the underlying structure of this fractal basin boundary by applying the straddle orbit method. However, there remain some important unanswered questions about this fractal structure which we hope to investigate the coming year.Recently a new fundamental phenomenon in nonlinear dynamics has been discovered by the investigators : catastrophic bifurcations causing loss of stability followed by chao … More tic transients leading to one of several possible new attractor outcomes. In this project the ideas were pursued further to discover additional types of bifurcations with indeterminate outcome, according to the form of the initiating bifurcation. In addition to the already-known indeterminate saddle-node and chaotic blue sky catastrophe, new types include indeterminate transcritical and subcritical bifurcations have been discovered. These appear in simple prototypical nonlinear oscillators modelling forced oscillations in a potential well. Engineering applications include the capsize of ships in heavy seas. It appears that these phenomena are common and widespread in engineering problems.Another nonlinear oscillator describing a proposed ship stabilization mechanism was studied, again using digital simulation and dynamical systems approaches. This oscillator includes a time delay term ; it was found that the destabilization of the system by gradually increasing the feedback gain results in the development of almost periodic oscillations and then chaotic behavior which is an immediate precursor of capsize. Less

利用基于动力系统几何理论的数字模拟和算法，研究了代表两个耦合摆动动态的常微分方程。这些方程是从一个简单的发电系统的动态稳定性的一个简单的模型，包括两个发电机连接的传输线。虽然该系统没有混沌吸引子，但存在一个分形流域边界，这在确定工程稳定性方面具有重要意义。应用跨轨法，在理解这种分形盆地边界的底层结构方面取得了实质性进展。然而，关于这种分形结构仍然存在一些重要的未解问题，我们希望在明年对此进行研究。最近，研究人员发现了非线性动力学中的一个新的基本现象：导致稳定性丧失的灾难性分叉，随后是混乱 ...更多信息 tic瞬变导致几种可能的新吸引子结果之一。在这个项目中，进一步追求的想法，发现其他类型的分叉与不确定的结果，根据形式的起始分叉。除了已知的不确定鞍结和混沌蓝天突变外，还发现了新的不确定跨临界和亚临界分岔。这些出现在简单的原型非线性振荡器模拟强迫振荡的潜力。工程应用包括船舶在波涛汹涌的大海中倾覆。这些现象在工程问题中是普遍存在的，本文利用数字仿真和动力系统方法研究了另一种描述船舶减摇机理的非线性振子。该振荡器包括一个时间延迟项，它被发现，通过逐渐增加的反馈增益的系统的不稳定的结果在几乎周期性振荡的发展，然后混沌行为，这是倾覆的直接前兆。少

项目成果

上田 よし亮,則安 学,H.B.Stewart: "來叉軌道法による引力圏境の根元集合の解析" 電子情報通信学会非線形問題研究会資料. NLP91ー43. 45-52 (1991)

Yoshiaki Ueda、Manabu Noriyasu、H.B.Stewart：“使用交叉轨道方法分析引力类别边界的根集”IEICE 非线性问题研究组材料。 ​​45-52 (1991)。

Toshisuke Ueda, Tadashi Mitsi and J. M. T. Thompson: "On Bifurcation Phenomena in a Nonlinear System with Delay Time" IEICE Technical Report. 91-353. 53-59 (1991)

Toshisuke Ueda、Tadashi Mitsi 和 J. M. T. Thompson：“具有延迟时间的非线性系统中的分岔现象”IEICE 技术报告。

上田 よし亮,三井 正,J.M.T.Thompson: "遅延時間を含む非線形系の初期関数問題" 1992年電子情報通信学会春季大学. 1-70 (1992)

Yoshiaki Ueda、Tadashi Mitsui、J.M.T.Thompson：“包括延迟时间在内的非线性系统的初始函数问题”1992 年春季大学电子、信息和通信工程师研究所 1-70 (1992)。

Yoshisuke Ueda, Manabu Noriyasu and H. Bruce Stewart: "Analysis of Basic Sets on Basin Boundaries Using Straddle Orbit Method" IEICE Technical Report. 91-352. 45-52 (1991)

Yoshisuke Ueda、Manabu Noriyasu 和 H. Bruce Stewart：“使用跨轨道方法分析盆地边界基本集”IEICE 技术报告。

上田 よし亮,三井 正,J.M.T.Thompson: "遅延時間を含む非線形系の分岐現象について" 電子情報通信学会非線形問題研究会資料. NLP91ー44. 53-59 (1991)

Yoshiaki Ueda、Tadashi Mitsui、J.M.T.Thompson：“关于非线性系统中的分岔现象，包括延迟时间”IEICE 非线性问题研究组材料。 ​​53-59 (1991)。