A rigorous formalism of information transfer between dynamical system components. I. Discrete mapping

X. San Liang, Richard Kleeman

Research output: Contribution to journalArticlepeer-review

Abstract

We put the concept of information transfer on a rigorous footing and establish for it a formalism within the framework of discrete maps. The resulting transfer measure possesses a property of directionality or transfer asymmetry as emphasized by Schreiber [T. Schreiber, Measuring information transfer, Phys. Rev. Lett. 85 (2) (2000) 461]; it also verifies the transfer measure for two-dimensional systems, which was obtained by Liang and Kleeman [X.S. Liang, R. Kleeman, Information transfer between dynamical system components, Phys. Rev. Lett. 95 (24) (2005) 244101] through a different avenue. Connections to classical formalisms are explored and applications presented. We find that, in the context of the baker transformation, there is always information flowing from the stretching direction to the folding direction, while no transfer occurs in the opposite direction; we also find that, within the Hénon map system, the transfer from the quadratic component to the linear component is of a simple form as expected on physical grounds. This latter result is unique to our formalism.

Original languageEnglish (US)
Pages (from-to)1-9
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume231
Issue number1
DOIs
StatePublished - Jul 1 2007

Keywords

  • Baker transformation
  • Frobenius-Perron operator
  • Hénon map
  • Information transfer

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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