Generation and Dynamics Analysis of N-Scroll Existence via Four Different Functions in Translation Chaotic System

Abstract

In the three-dimensional ordinary differential equations, a systematic methodology for generating and designing N-scroll chaotic attractors have been proposed by Liu in 2016, which was named the translation chaotic system and the translation transformation principle, respectively. In this paper, generation N-scroll existence four different functions are been proposed. They are absolute function, sign function, the piecewise and hyperbolic function. Then, the dynamics properties in the chaotic system via different methods are investigated in detail. Furthermore, MATLAB simulation results show that these methods emerge similar but topologically non-equivalent chaotic attractors.

Antimonotonicity, Chaos and Multidirectional Scroll Attractor in Autonomous ODEs Chaotic System

“…As we all know, because of the chaotic behavior and double scroll attractor, Chua circuit has obtained wide-spread attention all over the world [20]. Subsequently, many literatures were found the various types of scroll attractors are based on nonlinear function, such as the sinusoidal [16], trigonometric [17], transformations [18], piecewise [19], [23], saturation, sign [20]- [22], tangent, multi-fold surface, wings forms of scroll attractors [25], and so on [21]- [24]. However, the highly complex dynamics, such as antimonotonicity [26]- [28] and coexisting attractors [29], [30], [35], [44], as a new research direction, are…”