LYAPUNOV EXPONENTS OF THE KURAMOTO-SIVASHINSKY PDE

被引：21

作者：

Edson, Russell A. ^{[1
]}

Bunder, J. E. ^{[1
]}

Mattner, Trent W. ^{[1
]}

Roberts, A. J. ^{[1
]}

机构：

[1] Univ Adelaide, Sch Math Sci, Adelaide, SA, Australia

来源：

ANZIAM JOURNAL | 2019年 / 61卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Lyapunov exponents; dynamical systems; COMPUTATION; EQUATION; CHAOS; FLOW;

D O I：

10.1017/S1446181119000105

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Kuramoto-Sivashinsky equation is a prototypical chaotic nonlinear partial differential equation (PDE) in which the size of the spatial domain plays the role of a bifurcation parameter. We investigate the changing dynamics of the Kuramoto-Sivashinsky PDE by calculating the Lyapunov spectra over a large range of domain sizes. Our comprehensive computation and analysis of the Lyapunov exponents and the associated Kaplan-Yorke dimension provides new insights into the chaotic dynamics of the Kuramoto-Sivashinsky PDE, and the transition to its one-dimensional turbulence.

引用

页码：270 / 285

页数：16

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