Simulating a Chaotic Process

Celso Grebogi, R. L. Viana, J. R. R. Barbosa, A. M. Batista, E. M. Braz

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Abstract

Computer simulations of partial differential equations of mathematical physics typically lead to some kind of high-dimensional dynamical system. When there is chaotic behavior we are faced with fundamental dynamical difficulties. We choose as a paradigm of such high-dimensional system a kicked double rotor. This system is investigated for parameter values at which it is strongly non-hyperbolic through a mechanism called unstable dimension variability, through which there are periodic orbits embedded in a chaotic attractor with different numbers of unstable directions. Our numerical investigation is primarily based on the analysis of the finite-time Lyapunov exponents, which gives us useful hints about the onset and evolution of unstable dimension variability for the double rotor map, as a system parameter (the forcing amplitude) is varied.

Original languageEnglish
Pages (from-to)139-147
Number of pages8
JournalBrazilian Journal of Physics
Volume35
Publication statusPublished - 2005

Keywords

  • UNSTABLE DIMENSION VARIABILITY
  • LYAPUNOV EXPONENTS
  • DYNAMIC-SYSTEMS
  • SYNCHRONIZATION
  • TRAJECTORIES

Cite this

Grebogi, C., Viana, R. L., Barbosa, J. R. R., Batista, A. M., & Braz, E. M. (2005). Simulating a Chaotic Process. Brazilian Journal of Physics, 35, 139-147.