A scaling law chaotic system

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.

arXiv comment18 pages, 21 figures, 15 references Keywords: Fractal; Chaos; Mandelbrot Scaling Law; Scaling-Law Ordinary Differential Equation; Fractal Dimension