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.Comment: 18 pages, 21 figures, 15 references Keywords: Fractal; Chaos; Mandelbrot Scaling Law; Scaling-Law Ordinary Differential Equation; Fractal Dimensio
Over the last decade, the chaotic behaviors of dynamical systems have been extensively explored. Rec...
We have introduced to the problem of chaotic diffusion generated by deterministic dynamical systems....
A new approach to understanding nonlinear dynamics and strange attractors. The behavior of a physica...
Chaos theory is the study of change over time, specifically of highly volatile, seemingly random sit...
Proceedings of The Symposium on Applied Mathematics : Wavelet, Chaos and Nonlinear PDEs / Edited by ...
Contents: 0. Introduction 149 3.6. A thermodynamical formalism for unidimensional-1. Chaotic attract...
This presentation applies concepts in fractal geometry to the relatively new field of mathematics kn...
A paraphrase of Tolstoy that has become popular in the field of nonlinear dynamics is that while all...
We develop a quantitative microscopic theory of decaying Turbulence by studying the dimensional redu...
Both fractal geometry and dynamical systems have a long history of development and have provided fer...
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems wit...
In this dissertation a study is made of chaotic behaviour, the bifurcation sequences leading to chao...
The box counting dimension $\mathit{d_{C}}$ and the correlation dimension $\mathit{d_{G}}$ change wi...
Chaotic dynamics occur in deterministic systems which display extreme sensitivity on initial conditi...
ACKNOWLEDGMENTS We sincerely thank the people who gave valuable comments. This paper was supported b...
Over the last decade, the chaotic behaviors of dynamical systems have been extensively explored. Rec...
We have introduced to the problem of chaotic diffusion generated by deterministic dynamical systems....
A new approach to understanding nonlinear dynamics and strange attractors. The behavior of a physica...
Chaos theory is the study of change over time, specifically of highly volatile, seemingly random sit...
Proceedings of The Symposium on Applied Mathematics : Wavelet, Chaos and Nonlinear PDEs / Edited by ...
Contents: 0. Introduction 149 3.6. A thermodynamical formalism for unidimensional-1. Chaotic attract...
This presentation applies concepts in fractal geometry to the relatively new field of mathematics kn...
A paraphrase of Tolstoy that has become popular in the field of nonlinear dynamics is that while all...
We develop a quantitative microscopic theory of decaying Turbulence by studying the dimensional redu...
Both fractal geometry and dynamical systems have a long history of development and have provided fer...
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems wit...
In this dissertation a study is made of chaotic behaviour, the bifurcation sequences leading to chao...
The box counting dimension $\mathit{d_{C}}$ and the correlation dimension $\mathit{d_{G}}$ change wi...
Chaotic dynamics occur in deterministic systems which display extreme sensitivity on initial conditi...
ACKNOWLEDGMENTS We sincerely thank the people who gave valuable comments. This paper was supported b...
Over the last decade, the chaotic behaviors of dynamical systems have been extensively explored. Rec...
We have introduced to the problem of chaotic diffusion generated by deterministic dynamical systems....
A new approach to understanding nonlinear dynamics and strange attractors. The behavior of a physica...