Deterministic Diffusion — A Quality of Chaos
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.
KeywordsPower Spectrum Master Equation Excess Noise Diffusive Motion Invariant Distribution
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