A novel type of chaotic attractor with a multiunit structure: from multiscroll attractors to multi-bond orbital attractors
A novel type of chaotic attractor with a multiunit structure: from multiscroll attractors to multi-bond orbital attractors
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DOI：
10.1140/epjp/s13360-022-03268-4
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
Xin Zhang;Chuang Li
中科院分区：
文献类型：
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作者：
Xin Zhang;Chuang Li
传统的多单元结构混沌吸引子（MUCAs）在单元结构拓扑方面主要局限于几种常规拓扑（涡旋、机翼和环面）。近年来，一种新兴的具有键轨道拓扑和可扩展单元结构的混沌吸引子被发现，它属于但又不同于传统的自激muca，由于其键轨道拓扑优势，被命名为键轨道混沌吸引子（BOCA）。本文继续对这一现象进行深入探索，挖掘在更简单的系统中产生具有电路可复制基础的多键轨道混沌吸引子（MBOCA）的方法，并给出了探索过程。利用相图、LE谱、时域波形图、分岔图、引力盆地、庞加莱图等多种动态数值计算和分析方法，以及平衡计算和稳定性定量分析、本征面和本征向量计算、对称性和耗散分析等方法，对boca或其周期性对应物进行有针对性的研究。最后，与常规SE muca进行了对比分析，总结并列举了(M) boca的一些特性。总之，混沌吸引子这种新现象的出现打破了长期建立的MUCA框架，并表现出一些新的动力学行为。换句话说，本文的研究可以为SE MUCA家族增加一名新成员，为基于混沌的加密应用提供另一类候选对象，甚至为SE混沌吸引子和MUCA的研究打开一扇新的大门。
Traditional multiunit structure chaotic attractors (MUCAs) are mainly limited to several routine topologies (scroll, wing, and torus) in terms of unit structure topology. Recently, an emerging chaotic attractor with bond orbital topology and scalable unit structure was discovered, which belongs to but is different from conventional self-excited (SE) MUCAs, and was named as bond orbital chaotic attractor (BOCA) due its dominant bond orbital topology. This paper continues the in-depth exploration of this phenomenon, mining methods to generate multi-bond orbital chaotic attractor (MBOCA) with a circuit-reproducible basis in a simpler system, and presents the exploration process. Various dynamic numerical calculation and analysis methods, such as phase portraits, LE spectra, time-domain waveform diagrams, bifurcation diagrams, attraction basins, and Poincare maps, as well as equilibrium calculation and quantitative analysis for stability, eigenplane and eigenvector calculation, symmetry and dissipation analysis, have been exploited to conduct targeted research on the BOCAs or its periodic counterpart. Finally, a comparative analysis with routine SE MUCAs is performed, and some properties of (M)BOCAs are summarized and listed. In a word, the emergence of this new phenomenon of chaotic attractor breaks the long-established MUCA framework and exhibits some novel dynamical behaviors. In other words, the research in this paper can add a new member to the SE MUCA family, provide another class of candidates for chaos-based encryption applications, and even open a new door for the study of SE chaotic attractors and MUCAs.