• Effect of boundary conditions on the invariant density of noisy maps at fully-developed chaos

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/048/01/0109-0128

    • Keywords

       

      One-dimensional maps; fully developed chaos; invariant density; boundary conditions; noise

    • Abstract

       

      The invariant density of one-dimensional maps in the regime of fully-developed chaos with uncorrelated additive noise is considered. Boundary conditions are shown to play a significant role in determining the precise form of the invariant density, via the manner in which they handle the spill-over, caused by the noise, of orbits beyond the interval. The known case of periodic boundary conditions is briefly recapitulated. Analytic solutions for the invariant density that are possible under certain conditions are presented with applications to specific well-known maps. The case of ‘sticky’ boundaries is generalized to ‘re-injection at the nearest boundary’, and the exact functional equations determining the invariant density are derived. Interesting boundary layer effects are shown to occur, that lead to significant modifications of the invariant density corresponding to the unperturbed (noise-free) case, even when the latter is a constant — as illustrated by an application of the formalism to the noisy tent map. All our results are non-perturbative, and hold good for any noise amplitude in the interval.

    • Author Affiliations

       

      V Balakrishnan1 G Nicolis1 2 C Nicolis1 3

      1. Department of Physics, Indian Institute of Technology, Madras - 600 036, India
      2. Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, C.P. 231, Bruxelles - 1050, Belgium
      3. Institut Royal Météorologique de Belgique, Bruxelles - 1180, Belgium
    • Dates

       
  • Pramana – Journal of Physics | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.