Generation of 2N + 1-scroll existence in new three-dimensional chaos systems

Generation and dynamics analysis of N-scrolls existence in new translation-type chaotic systems

In this paper, we propose two kinds of translation type chaotic systems for creating 2 N + 1-and 2(N + 1)-scrolls chaotic attractors from a simple three-dimensional system, which are named the translation-2 chaotic system (a₁₂a₂₁ < 0) and the translation-3 chaotic system (a₁₂a₂₁ > 0). We also propose the successful design criterion for constructing 2 N + 1-and 2(N + 1)-scrolls, respectively. Then, the dynamics property of the translation-2 chaotic system is studied in detail. MATLAB simulation results show that very sophisticated dynamical behaviors and unique chaotic behaviors of the system. Finally, the definition and criterion of multi-scroll attractors for the translation-3 chaotic system is obtained. Three representative examples are shown in some classical chaotic systems that can be equally obtained via the set parameters of the translation type chaotic system. Furthermore, we show that the translation type chaotic systems have similar but topologically non-equivalent chaotic attractors, and they are the three-dimensional ordinary differential equations.

Preface: Recent Advances in Fractional Dynamics

This Special Focus Issue contains several recent developments and advances on the subject of Fractional Dynamics and its widespread applications in various areas of the mathematical, physical, and engineering sciences.