{"title":"Matryoshka multistability: Coexistence of an infinite number of exactly self-similar nested attractors in a fractal phase space","authors":"","doi":"10.1016/j.chaos.2024.115412","DOIUrl":null,"url":null,"abstract":"<div><p>Multistability, and its special types such as megastability and extreme multistability, is an important phenomenon in modern nonlinear science that provides several possible practical applications. In this paper, we propose a new special type of multistability when the infinite number of exactly self-similar attractors nested inside each other coexist in a system. We called it matryoshka multistability due to its resemblance to the famous Russian wooden doll. We theoretically explain and experimentally confirm the properties of a new type of multistable behavior using two representative examples based on the Chua and Sprott Case J chaotic systems. In addition, we construct an adaptive controller for synchronizing two Chua-type matryoshka multistable systems when the amplitude of the master system is of arbitrary scale. The proposed type of multistability can find several applications in chaotic communication, cryptography, and data compression.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3000,"publicationDate":"2024-08-26","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/S0960077924009640","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
Abstract
Multistability, and its special types such as megastability and extreme multistability, is an important phenomenon in modern nonlinear science that provides several possible practical applications. In this paper, we propose a new special type of multistability when the infinite number of exactly self-similar attractors nested inside each other coexist in a system. We called it matryoshka multistability due to its resemblance to the famous Russian wooden doll. We theoretically explain and experimentally confirm the properties of a new type of multistable behavior using two representative examples based on the Chua and Sprott Case J chaotic systems. In addition, we construct an adaptive controller for synchronizing two Chua-type matryoshka multistable systems when the amplitude of the master system is of arbitrary scale. The proposed type of multistability can find several applications in chaotic communication, cryptography, and data compression.
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.