Low-dimensional modelling of dynamical systems
Low-dimensional modelling of dynamical systems
复制标题
动力系统的低维建模
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
Anthony J. Roberts
中科院分区：
文献类型：
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作者：
Anthony J. Roberts
简要地考虑一下流体动力学方程，它们描述了流体流动中所有相互作用的物理要素的大量细节，而在应用中，我们只想描述那些有趣的东西。在各种各样的情况下，需要简单的近似模型来进行实际模拟和预测。我回顾推导，从数学描述的详细动态，准确，完整和有用的低维模型的有趣的动态系统。中心流形理论和相关技术的发展使这一建模过程有了坚实的基础。如Guckenheinmer & Holmes [79，§2.5]：
Consider briefly the equations of fluid dynamics—they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow—whereas in applications we want to deal with a description of just that which is interesting. In a wide variety of situations, simple approximate models are needed to perform practical simulations and make forecasts. I review the derivation, from a mathematical description of the detailed dynamics, of accurate, complete and useful low-dimensional models of the interesting dynamics in a system. The development of centre manifold theory and associated techniques puts this modelling process on a firm basis. As in Guckenheinmer & Holmes [79, §2.5]: