A scaling law chaotic system
Xiao-Jun Yang (School of Mathematics, China University of Mining and, Technology, Xuzhou, China)
TL;DR
This paper introduces a novel chaotic system based on scaling-law differential equations involving Mandelbrot scaling, exhibiting unique behaviors and comparing it with classical attractors, potentially advancing chaos theory.
Contribution
It proposes a new scaling-law chaotic system incorporating Mandelbrot scaling, with analysis of its behavior and a conjecture on fixed point theory for fractal attractors.
Findings
Demonstrates a new chaotic system with Mandelbrot scaling law
Shows the 'Wukong' effect in the proposed chaos
Provides comparison with Lorenz attractors
Abstract
In this article, we propose an anomalous chaotic system of the scaling-law ordinary differential equations involving the Mandelbrot scaling law. This chaotic behavior shows the "Wukong" effect. The comparison among the Lorenz and scaling-law attractors is discussed in detail. We also suggest the conjecture for the fixed point theory for the fractal SL attractor. The scaling-law chaos may be open a new door in the study of the chaos theory.
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