How long do numerical chaotic solutions remain valid?

被引：118

作者：

Sauer, T

Grebogi, C

Yorke, JA

机构：

[1] UNIV MARYLAND,INST PHYS SCI & TECHNOL,COLLEGE PK,MD 20742

[2] UNIV POTSDAM,INST THEORET PHYS & ASTROPHYS,D-14415 POTSDAM,GERMANY

[3] UNIV MARYLAND,INST PLASMA RES,COLLEGE PK,MD 20742

来源：

PHYSICAL REVIEW LETTERS | 1997年 / 79卷 / 01期

关键词：

D O I：

10.1103/PhysRevLett.79.59

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Dynamical conditions for the loss of validity of numerical chaotic solutions of physical systems are already understood. However, the fundamental questions of ''how good'' and ''for how long'' the solutions are valid remained unanswered. This work answers these questions by establishing scaling laws for the shadowing distance and for the shadowing time in terms of physically meaningful quantities that are easily computable in practice. The scaling theory is verified against a physical model.

引用

页码：59 / 62

页数：4

共 12 条

[1]

Abraham R., 1970, P S PURE MATH, V14, P5

[2]

Anosov D. V., 1967, T MAT I STEKLOV, V90

[3]

BOWEN R, 1975, J DIFFER EQUATIONS, V18, P333, DOI 10.1016/0022-0396(75)90065-0

[4] OBSTRUCTIONS TO SHADOWING WHEN A LYAPUNOV EXPONENT FLUCTUATES ABOUT ZERO [J].