权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Chaotic Phenomena and Their Engineering Relevance

混沌现象及其工程相关性

基本信息

批准号：
05044091
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：
1993
资助国家：
日本
起止时间：
1993 至无数据
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-05044091/
关键词：
Nolinear dynamical systems Simulation experiments Bifurcation Indeterminate outcome Minorsky equation Basin boundary Straddle orbit method 位相同期系

项目摘要

The objective of research is to understand the behavior of nonlinear dynamical systems using theory and extensive numerical simulation. Prototype models including second-order oscillators have been selected to include some previously neglected but essential properties of real physical and engineering systems. Basic insight is gained by avoided unnecessary camplications.A comprehensive review and classification of hifurcations involving one parameter was completed. Safe, explosive and dangerous types were distinguished, and related to phenomena of fundamental concern in applications : continuity or discontinuity of responses, hysteresis, intermittency and indeterminate outcomes. Study of escape from potential wells was extended to a wide range of volues of the damping coefficient. The close connection between optimal escape and resonance was confirmed ; subtle but important changes in bifurcation patterns were discovered, and their significance for experimental studies was clarified.We have considered the nonlinear dynamical system with time delay described by the Minorsky equation (see Minorsky, J.Appl.Phys, Vol.19, 1948), which he introduced during his studies of active ship stabilization. Differential equations with a time delay, sometimes called differential-difference equations, have an infinite dimensional phase space. The global features of the basin boundaries are not easily grasped, but they have great practical importance.In earlier work, we made some progress by making 'carpet bombing' experiments from a grid of starts in one cross-section of the phase space : but now we have focused attention on the unstable basic sets governing the basin boundaries, which we have located numerically using the straddle orbit technique. This approach gives much more insight into basin structure than carpet bombing ; for example, a stability index involving distance from attracter to unstable basic set may be computed. This will be pursued in future research.

研究的目的是利用理论和广泛的数值模拟来理解非线性动力系统的行为。包括二阶振子的原型模型已被选定，包括一些以前被忽视的，但真实的物理和工程系统的基本属性。通过避免不必要的复杂性，获得了基本的认识。对安全、爆炸和危险类型进行了区分，并与应用中的基本关切现象有关：反应的连续性或不连续性、滞后性、不稳定性和不确定的结果。将势威尔斯逃逸的研究扩展到阻尼系数的宽范围。最优逃逸和共振之间的密切联系被证实;分叉模式的微妙但重要的变化被发现，并阐明了它们对实验研究的意义。我们考虑了由Minorsky方程（见Minorsky，J.Appl.Phys，Vol.19，1948）描述的具有时滞的非线性动力系统，他在主动船舶稳定性研究中引入了该方程。具有时滞的微分方程，有时称为微分差分方程，具有无限维的相空间。盆地边界的全局特征不易把握，但它们具有很大的实际意义。在早期的工作中，我们通过在相空间的一个横截面上从网格开始进行“地毯式轰炸”实验取得了一些进展：但现在我们已经将注意力集中在控制盆地边界的不稳定基本集上，我们已经使用跨轨技术对它们进行了数值定位。这种方法比地毯式轰炸对盆地结构有更多的了解;例如，可以计算涉及从吸引子到不稳定基本集的距离的稳定性指数。这将在今后的研究中继续进行。