Necessity of statistical modeling of deterministic chaotic systems

Y C Lai, C Grebogi, Ying-Cheng Lai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The success of deterministic modeling of a physical system relies on whether the solution of the model would approximate the dynamics of the actual system. When the system is chaotic, situations can arise where periodic orbits embedded in the chaotic set have distinct number of unstable directions, a dynamical property known as unstable dimension variability. As a consequence, no model of the system produces reasonably long trajectories that are realized by nature. We argue and present physical examples indicating that, in such a case, though the model is deterministic and low-dimensional, statistical quantities can still be reliably computed. We also argue that unstable dimension variability may be common in high-dimensional chaotic systems such as those arising from discretization of nonlinear partial differential equations.

Original languageEnglish
Title of host publicationSTATISTICAL PHYSICS
EditorsM Tokuyama, HE Stanley
Place of PublicationMELVILLE
PublisherAMER INST PHYSICS
Pages531-542
Number of pages12
ISBN (Print)1-56396-940-8
Publication statusPublished - 2000
Event3rd Tohwa University International Conference on Statistical Physics - FUKUOKA
Duration: 9 Nov 199912 Nov 1999

Conference

Conference3rd Tohwa University International Conference on Statistical Physics
CityFUKUOKA
Period9/11/9912/11/99

Keywords

  • UNSTABLE DIMENSION VARIABILITY
  • TRANSVERSE INSTABILITY
  • DYNAMIC-SYSTEMS
  • TRAJECTORIES
  • OSCILLATORS
  • ATTRACTORS
  • ORBITS

Cite this

Lai, Y. C., Grebogi, C., & Lai, Y-C. (2000). Necessity of statistical modeling of deterministic chaotic systems. In M. Tokuyama, & HE. Stanley (Eds.), STATISTICAL PHYSICS (pp. 531-542). AMER INST PHYSICS.