{"title":"混沌图中的循环对称动力学","authors":"Jin Liu , Kehui Sun , Huihai Wang","doi":"10.1016/j.chaos.2024.115684","DOIUrl":null,"url":null,"abstract":"<div><div>In a recent paper (Liu et al., 2024), we reported on the microscopic mechanism underlying multistability in discrete dynamical systems, suggesting the potential for higher, even arbitrary-dimensional multistability in our conclusions. Before we can validate it, a fundamental question arises: what method can preserve the global dynamics of systems while allowing for an increase in dimensionality? This paper identifies the cyclic symmetric structure as a crucial solution and establishes two two-dimensional maps model based on it. The presence of multistability in any direction is affirmed, with this phenomenon representing either homogeneous or heterogeneous infinite expansion of the medium in multidimensional space. Furthermore, we uncover a range of dynamical characteristics, including grid-like phase trajectories, scale-free attractor clusters, fractal basin structures, symmetric attractors, and chaotic diffusion, all rooted in the system’s symmetric dynamical nature. This research not only enhances the comprehension of high-dimensional symmetric dynamics, but also offers a novel perspective for elucidating related models and phenomena.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3000,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Cyclic symmetric dynamics in chaotic maps\",\"authors\":\"Jin Liu , Kehui Sun , Huihai Wang\",\"doi\":\"10.1016/j.chaos.2024.115684\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In a recent paper (Liu et al., 2024), we reported on the microscopic mechanism underlying multistability in discrete dynamical systems, suggesting the potential for higher, even arbitrary-dimensional multistability in our conclusions. Before we can validate it, a fundamental question arises: what method can preserve the global dynamics of systems while allowing for an increase in dimensionality? This paper identifies the cyclic symmetric structure as a crucial solution and establishes two two-dimensional maps model based on it. The presence of multistability in any direction is affirmed, with this phenomenon representing either homogeneous or heterogeneous infinite expansion of the medium in multidimensional space. Furthermore, we uncover a range of dynamical characteristics, including grid-like phase trajectories, scale-free attractor clusters, fractal basin structures, symmetric attractors, and chaotic diffusion, all rooted in the system’s symmetric dynamical nature. This research not only enhances the comprehension of high-dimensional symmetric dynamics, but also offers a novel perspective for elucidating related models and phenomena.</div></div>\",\"PeriodicalId\":9764,\"journal\":{\"name\":\"Chaos Solitons & Fractals\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.3000,\"publicationDate\":\"2024-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos Solitons & Fractals\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0960077924012360\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0960077924012360","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
摘要
在最近的一篇论文(Liu et al., 2024)中,我们报告了离散动力系统多稳定性的微观机制,并在结论中提出了更高、甚至任意维度多稳定性的可能性。在我们验证它之前,一个基本问题出现了:什么方法既能保持系统的全局动力学,又能允许维度的增加?本文认为循环对称结构是一个重要的解决方案,并在此基础上建立了两个二维映射模型。本文肯定了任何方向上的多稳定性的存在,这种现象代表了介质在多维空间中的同质或异质无限扩展。此外,我们还发现了一系列动力学特征,包括网格状相轨迹、无标度吸引子簇、分形盆地结构、对称吸引子和混沌扩散,所有这些都植根于系统的对称动力学性质。这项研究不仅加深了对高维对称动力学的理解,还为阐明相关模型和现象提供了新的视角。
In a recent paper (Liu et al., 2024), we reported on the microscopic mechanism underlying multistability in discrete dynamical systems, suggesting the potential for higher, even arbitrary-dimensional multistability in our conclusions. Before we can validate it, a fundamental question arises: what method can preserve the global dynamics of systems while allowing for an increase in dimensionality? This paper identifies the cyclic symmetric structure as a crucial solution and establishes two two-dimensional maps model based on it. The presence of multistability in any direction is affirmed, with this phenomenon representing either homogeneous or heterogeneous infinite expansion of the medium in multidimensional space. Furthermore, we uncover a range of dynamical characteristics, including grid-like phase trajectories, scale-free attractor clusters, fractal basin structures, symmetric attractors, and chaotic diffusion, all rooted in the system’s symmetric dynamical nature. This research not only enhances the comprehension of high-dimensional symmetric dynamics, but also offers a novel perspective for elucidating related models and phenomena.
期刊介绍:
Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.