Dynamical characteristics of discretized chaotic permutations

Naoki Masuda*, Kazuyuki Aihara

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


Chaos theory has been applied to various fields where appropriate random sequences are required. The randomness of chaotic sequences is characteristic of continuous-state systems. Accordingly, the discrepancy between the characteristics of spatially discretized chaotic dynamics and those of original analog dynamics must be bridged to justify applications of digital orbits generated, for example, from digital computers simulating continuous-state chaos. The present paper deals with the chaotic permutations appearing in a chaotic cryptosystem. By analysis of cycle statistics, the convergence of the invariant measure and periodic orbit skeletonization, we show that the orbits in chaotic permutations are ergodic and chaotic enough for applications. In the consequence, the systematic differences in the invariant measures and in the Lyapunov exponents of two infinitesimally L-close maps are also investigated.

Original languageEnglish
Pages (from-to)2087-2103
Number of pages17
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number10
Publication statusPublished - 2002 Oct
Externally publishedYes


  • Chaotic cryptosystem
  • Discretization
  • Dynamical system
  • Skew tent map

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


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