二维非双曲平衡点附近构造局部Lyapunov函数的数值验证方法

IF 0.4 Q4 MATHEMATICS, APPLIED

JSIAM Letters Pub Date : 2022-01-01 DOI:10.14495/jsiaml.14.33

Koki Nitta, Toshiki Sasaki, N. Yamamoto

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引用次数: 1

摘要

Terasaka等人。JSIAM列托人。(2020)，我们提出了数值验证方法，使用高达三次多项式的非线性变换在非双曲平衡点周围构造局部Lyapunov函数。在本研究中，我们扩展了这些方法，证明了任意次多项式可以用来定义变换，并给出了一个必须使用五次多项式来构造局部Lyapunov函数的示例问题。

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On numerical verification methods to construct local Lyapunov functions around non-hyperbolic equilibria for two-dimensional cases

In Terasaka et al. JSIAM Lett. (2020), we have proposed numerical veriﬁcation methods to construct local Lyapunov functions around non-hyperbolic equilibria using non-linear transformations by up to third degree polynomials. In the present study, we extend these methods by proving that polynomials of an arbitrary degree can be applied to deﬁne the transformations and show an example problem where we have to use a ﬁfth-degree polynomial to construct local Lyapunov functions.

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来源期刊

JSIAM Letters MATHEMATICS, APPLIED-

自引率

25.00%

发文量