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Fractal Evolution of Normalized Feedback Systems on a Lattice

Siegfried Fussy·Gerhard Groessing·Herbert Schwabl
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Abstract

Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter. It is shown that the combination of two operations, i.e. i) enhancement of a site's value when fulfilling a feedback condition and ii) normalization of the system after each time step, produces relatively short-lived spatio-temporal patterns whose mean lifetime can be considered as emergent order parameter of the system. This mean lifetime obeys a scaling law involving a control parameter which tunes the "fault tolerance" of the feedback condition. Thus, within appropriate ranges of the systems variables, the dynamical properties can be characterized by a "fractal evolution dimension" (as opposed to a "fractal dimension").

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Siegfried Fussy, Gerhard Groessing, Herbert Schwabl. 2002-04-18. Fractal Evolution of Normalized Feedback Systems on a Lattice. https://arxiv.org/abs/nlin/0204047

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