随机Bautin分岔系统的极大Lyapunov指数

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-03-07 DOI:10.1111/sapm.70035

Diandian Tang, Jingli Ren

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引用次数: 0

摘要

本文研究了具有加性白噪声的Bautin分岔系统的极大Lyapunov指数，该分岔系统也是无噪声情况下广义Hopf分岔的五阶截断范式。通过求解与系统不变测度相关的平稳密度及其边际分布，证明了最大Lyapunov指数随参数的变化具有不定符号，并给出了控制最大Lyapunov指数取值范围的显式条件。最后给出了小噪声极限下最大Lyapunov指数的渐近展开式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Maximal Lyapunov Exponent of a Stochastic Bautin Bifurcation System

In this paper, we investigate the maximal Lyapunov exponent of a Bautin bifurcation system with additive white noise, which is also the fifth-order truncated normal form of a generalized Hopf bifurcation in the absence of noise. By solving the stationary density associated with the invariant measure of the system and its marginal distribution, we show that the maximal Lyapunov exponent is of indefinite sign depending on parameters and we give the explicit condition to control the range of the maximal Lyapunov exponent. Finally, we give the asymptotic expansion of the maximal Lyapunov exponent in the small noise limit.

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.