OBSTRUCTIONS TO SHADOWING WHEN A LYAPUNOV EXPONENT FLUCTUATES ABOUT ZERO

S  DAWSON; C  GREBOGI; T  SAUER; J A  YORKE

OBSTRUCTIONS TO SHADOWING WHEN A LYAPUNOV EXPONENT FLUCTUATES ABOUT ZERO

S DAWSON, C GREBOGI, T SAUER, J A YORKE

Research output: Contribution to journal › Article › peer-review

Abstract

We study the existence or nonexistence of true trajectories of chaotic dynamical systems that lie close to computer-generated trajectories. The nonexistence of such shadowing trajectories is caused by finite-time Lyapunov exponents of the system fluctuating about zero. A dynamical mechanism of the unshadowability is explained through a theoretical model and identified in simulations of a typical physical system. The problem of fluctuating Lyapunov exponents is expected to be common in simulations of higher-dimensional systems.

Original language	English
Pages (from-to)	1927-1930
Number of pages	4
Journal	Physical Review Letters
Volume	73
Issue number	14
Publication status	Published - 3 Oct 1994

Keywords

DYNAMIC-SYSTEMS
TRAJECTORIES

Cite this

@article{2332c69efc0f4bbb94040e45173db71b,

title = "OBSTRUCTIONS TO SHADOWING WHEN A LYAPUNOV EXPONENT FLUCTUATES ABOUT ZERO",

abstract = "We study the existence or nonexistence of true trajectories of chaotic dynamical systems that lie close to computer-generated trajectories. The nonexistence of such shadowing trajectories is caused by finite-time Lyapunov exponents of the system fluctuating about zero. A dynamical mechanism of the unshadowability is explained through a theoretical model and identified in simulations of a typical physical system. The problem of fluctuating Lyapunov exponents is expected to be common in simulations of higher-dimensional systems.",

keywords = "DYNAMIC-SYSTEMS, TRAJECTORIES",

author = "S DAWSON and C GREBOGI and T SAUER and YORKE, {J A}",

year = "1994",

month = oct,

day = "3",

language = "English",

volume = "73",

pages = "1927--1930",

journal = "Physical Review Letters",

issn = "0031-9007",

publisher = "American Physical Society",

number = "14",

}

TY - JOUR

T1 - OBSTRUCTIONS TO SHADOWING WHEN A LYAPUNOV EXPONENT FLUCTUATES ABOUT ZERO

AU - DAWSON, S

AU - GREBOGI, C

AU - SAUER, T

AU - YORKE, J A

PY - 1994/10/3

Y1 - 1994/10/3

N2 - We study the existence or nonexistence of true trajectories of chaotic dynamical systems that lie close to computer-generated trajectories. The nonexistence of such shadowing trajectories is caused by finite-time Lyapunov exponents of the system fluctuating about zero. A dynamical mechanism of the unshadowability is explained through a theoretical model and identified in simulations of a typical physical system. The problem of fluctuating Lyapunov exponents is expected to be common in simulations of higher-dimensional systems.

AB - We study the existence or nonexistence of true trajectories of chaotic dynamical systems that lie close to computer-generated trajectories. The nonexistence of such shadowing trajectories is caused by finite-time Lyapunov exponents of the system fluctuating about zero. A dynamical mechanism of the unshadowability is explained through a theoretical model and identified in simulations of a typical physical system. The problem of fluctuating Lyapunov exponents is expected to be common in simulations of higher-dimensional systems.

KW - DYNAMIC-SYSTEMS

KW - TRAJECTORIES

M3 - Article

SN - 0031-9007

VL - 73

SP - 1927

EP - 1930

JO - Physical Review Letters

JF - Physical Review Letters

IS - 14

ER -

OBSTRUCTIONS TO SHADOWING WHEN A LYAPUNOV EXPONENT FLUCTUATES ABOUT ZERO

Abstract

Keywords

Fingerprint

Cite this