Hyperbolic structure for multiplicative noise saddle using Lagrangian descriptors

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-06-02 DOI:10.1016/j.cnsns.2025.108971

Huan Liao , Jiaopeng Yang

引用次数: 0

Abstract

This paper proposes a new concept, continuous stochastic Lagrangian descriptor, to discern the hyperbolic structure for multiplicative noise saddle and beyond. The multiplicative noise saddle is proved to entail a random fixed point with exponential dichotomy. Analogous to the additive noise case, the hyperbolic structures, composed of the random fixed point together with its stable and unstable manifolds, form barriers to transport in such a system. Moreover, the forward and backward components are compared to show the visible stable and/or unstable manifolds. We further discuss the capability of the discrete stochastic Lagrangian descriptor with the stochastic forced Duffing equation for the general systems driven by multiplicative noise.

查看原文本刊更多论文

使用拉格朗日描述符的乘性噪声鞍的双曲结构

本文提出了一个新的概念——连续随机拉格朗日描述子，用以识别乘性噪声鞍及其以外的双曲结构。证明了乘性噪声鞍包含一个指数二分类的随机不动点。与加性噪声情况类似，由随机不动点及其稳定和不稳定流形组成的双曲结构在这种系统中形成了传输障碍。此外，向前和向后的组件进行比较，以显示可见的稳定和/或不稳定流形。我们进一步讨论了离散随机拉格朗日描述子与随机强迫Duffing方程对于乘性噪声驱动的一般系统的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.