OBSTRUCTIONS TO SHADOWING WHEN A LYAPUNOV EXPONENT FLUCTUATES ABOUT ZERO

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

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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 languageEnglish
Pages (from-to)1927-1930
Number of pages4
JournalPhysical Review Letters
Volume73
Issue number14
Publication statusPublished - 3 Oct 1994

Keywords

  • DYNAMIC-SYSTEMS
  • TRAJECTORIES

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