A general method for generating multi-scroll and multi-wing chaotic systems and its implementation of attractor reproduction

吸引子 混乱的 纸卷 计算机科学 非线性系统 功能(生物学) 控制理论(社会学) 拓扑(电路) 数学 对称(几何) 数学分析 几何学 物理 人工智能 工程类 进化生物学 机械工程 生物 组合数学 量子力学 控制(管理)
作者
Ping He,Hongwei Liu,Guodong Li,Xiangliang Xu,Yujuan Gu
出处
期刊:Physica Scripta [IOP Publishing]
卷期号:98 (8): 085232-085232 被引量:1
标识
DOI:10.1088/1402-4896/ace6db
摘要

Abstract In comparison to traditional chaotic systems, the multi-scroll and multi-wing chaotic systems are more complicated. The design and execution of sophisticated multi-scroll or multi-wing chaotic attractors attract a lot of attention. However, these constructed nonlinear functions cannot be applied to extended multi-scroll and multi-wing attractors at the same time. To this end, this paper proposes a new function which can be used to generate multi-scroll and multi-wing chaotic attractors in both double-scroll and double-wing chaotic systems. Using this function, multi-scroll and multi-wing chaotic systems can be constructed directly without relying on whether the chaotic system has some symmetry (odd symmetry or even symmetry). The construction method presented is generally applicable to chaotic systems with multi-scroll and multi-wing self-excited attractors.The main point of this method is as follows: firstly, the piecewise linear (PWL) saturation function is nested within the cosine nonlinearity function , and the resulting nested COS-PWL function. Secondly, to enable the expansion of multi-wing and multi-scroll, the nested COS-PWL function is incorporated into the double-wing and double-scroll systems in different manners. The maximum Lyapunov exponent (MLE) and the bifurcation diagram route for increasing the number of wings and scrolls confirm the feasibility and effectiveness of the method. Finally, the three-element method is used to determine a Sinusoidal function, which can generate attractor self-reproduction in the corresponding dimension by replacing the state variables of the multi-scroll and multi-wing systems, so that an infinite number of coexisting attractors can be obtained by simply changing the initial values of the variables, i.e., multiple stability can be generated.
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