Journal of Statistical Physics

, Volume 63, Issue 3–4, pp 585–612 | Cite as

Noise-induced asymptotic periodicity in a piecewise linear map

  • Nicholas Provatas
  • Michael C. Mackey


We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.

Key words

Asymptotic periodicity asymptotic stability density evolution noise Keener map Boltzmann conditional entropy 


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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Nicholas Provatas
    • 1
  • Michael C. Mackey
    • 2
  1. 1.Department of Physics, and Center for Nonlinear DynamicsMcGill UniversityMontrealCanada
  2. 2.Departments of Physiology and Physics, and Center for Nonlinear DynamicsMcGill UniversityMontrealCanada

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