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Yang, Xiao-Jun

A scaling law chaotic system. (English) Zbl 1498.37063

Fractals 30, No. 3, Article ID 2250057, 8 p. (2022).
Summary: In this paper, we propose an anomalous chaotic system of the scaling-law (SL) ordinary differential equations involving the Mandelbrot SL. This chaotic behavior shows the “Wukong” effect. The comparison among the Lorenz and SL attractors is discussed in detail. We also suggest the conjecture for the fixed point theory for the fractal SL attractor. The SL chaos may be open a new door in the study of the chaos theory.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
28A80 Fractals

Keywords:

fractal; chaos; Mandelbrot scaling law; scaling-law ordinary differential equation; fractal dimension
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References:

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