SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 994-1028, January 2020.
The computational singular perturbation (CSP) method is an algorithm which iteratively approximates slow manifolds and fast fibers in multiple-timescale dynamical systems. Since its inception due to Lam and Goussis [Twenty-Second Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, 1989, pp. 931--941], the convergence of the CSP method has been explored in depth; however, rigorous applications have been confined to the standard framework, where the separation between “slow” and “fast” variables is made explicit in the dynamical system. This paper adapts the CSP method to nonstandard slow-fast systems having a normally hyperbolic attracting critical manifold. We give new formulas for the CSP method in this more general context, and provide the first concrete demonstrations of the method on genuinely nonstandard examples.

中文翻译：

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非标准慢速系统的计算奇异摄动法

SIAM应用动力系统杂志，第19卷，第2期，第994-1028页，2020年1月。
计算奇异摄动（CSP）方法是一种在多时标动力系统中迭代逼近慢流形和快纤维的算法。自从Lam和Goussis成立以来[第二十二届国际燃烧研讨会，宾夕法尼亚州匹兹堡，燃烧研究所，1989年，第931--941页]，已经深入探讨了CSP方法的收敛性。但是，严格的应用程序仅限于标准框架，其中在动态系统中明确了“慢”和“快”变量之间的分隔。本文将CSP方法应用于具有正常双曲线吸引临界流形的非标准慢速系统。在这种更一般的情况下，我们为CSP方法提供了新的公式，并在真正非标准的示例上首次提供了该方法的具体说明。