线性波动方程中的混沌

Q1 Mathematics

Chaos, Solitons and Fractals: X Pub Date : 2019-06-01 DOI:10.1016/j.csfx.2019.100014

Ned J. Corron

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引用次数: 2

摘要

一个线性偏微分方程显示了三个通常用来定义混沌动力学的性质。该系统包括一个一维波动方程，其增益作用于半无限线上。边界条件迫使波保持有限。结果表明，所得到的解集具有密集的周期轨道，包含传递轨道，并对初始条件具有极高的敏感性。根据这种线性混沌来考虑混沌的定义。

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Chaos in a linear wave equation

A linear partial differential equation is shown to exhibit three properties often used to define chaotic dynamics. The system comprises a one-dimensional wave equation with gain that operates on a semi-infinite line. A boundary condition enforces that the waves remain finite. It is shown that the resulting solution set is dense with periodic orbits, contains transitive orbits, and exhibits extreme sensitivity to initial conditions. Definitions of chaos are considered in light of such linear chaos.

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来源期刊

Chaos, Solitons and Fractals: X Mathematics-Mathematics (all)

CiteScore

5.00

自引率

0.00%

发文量

审稿时长

20 weeks