二维ODEs系统非双曲平衡的稳定性指标

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED Dynamical Systems-An International Journal Pub Date : 2022-03-18 DOI:10.1080/14689367.2022.2119941

Alexander Lohse

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引用次数: 1

摘要

我们将原点为0的二维常微分方程组的族视为非双曲平衡。对于任何数字，我们证明了在这些方程中选择一个参数是可能的，使得稳定性指数精确。与此相反，对于双曲平衡x，已知要么。此外，我们讨论了一个具有局部不稳定但全局吸引的平衡的系统，强调了局部和非局部稳定性指数之间的一些细微差异。

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Stability indices of non-hyperbolic equilibria in two-dimensional systems of ODEs

We consider families of systems of two-dimensional ordinary differential equations with the origin 0 as a non-hyperbolic equilibrium. For any number , we show that it is possible to choose a parameter in these equations such that the stability index is precisely . In contrast to that, for a hyperbolic equilibrium x it is known that either or . Furthermore, we discuss a system with an equilibrium that is locally unstable but globally attracting, highlighting some subtle differences between the local and non-local stability indices.

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来源期刊

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences