Deterministic Diffusion — A Quality of Chaos

  • T. Geisel
Part of the NATO ASI Series book series (NSSB, volume 116)


This paper reports on chaotic systems that can exhibit a deterministic “random” walk as an additional chaotic quality. This diffusive motion is generated within the dynamical system and not by external random forces. It is governed by a master equation, which is derived from an exact equation. The onset of diffusion is analogous to a phase transition and is described by a universal scaling function. Under certain circumstances the power spectra show excess noise at low frequencies and the mean-square displacements have an anomalous asymptotic behavior. In 2-dimensional systems there is a crossover in the critical behavior at the onset of diffusion.


Power Spectrum Master Equation Excess Noise Diffusive Motion Invariant Distribution 
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Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • T. Geisel
    • 1
  1. 1.Institut für Theoretische PhysikUniversität RegensburgRegensburgFederal Republic of Germany

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