{"title":"以共存吸引子和复杂多稳态行为为特征的忆阻多蝶混沌系统的设计与 FPGA 实现","authors":"Minxiu Yan, Peng Du","doi":"10.1140/epjp/s13360-024-05722-x","DOIUrl":null,"url":null,"abstract":"<div><p>Multibutterfly memristive chaotic systems (MMCSs) exhibit intricate multistable behavior and heightened randomness, making them highly advantageous for secure communications and image encryption. The paper provides a new five-dimensional chaotic system that incorporates two memristors into a 3D chaotic framework, leading to the creation of multibutterfly chaotic attractors. The quantity of multibutterfly chaotic attractors is capable of being managed by varying the parameters <span>\\(\\mathrm M\\)</span> and <span>\\(\\mathrm N\\)</span>. We conduct an in-depth analysis of the five-dimensional MMCS dynamics through methods like Lyapunov exponents, Poincare maps, phase diagrams, and bifurcation diagrams. We depicted the basin of attraction for exploring the system’s coexisting attractors. Furthermore, the five-dimensional MMCS exhibits the coexisting attractors through variations in the initial values. By tuning parameters <span>\\(k_{1}\\)</span> and <span>\\(k_{2}\\)</span>, the system’s amplitude can be adjusted. To validate the practical applicability of this system, we design a chaotic circuit based on the five-dimensional MMCS. The system is implemented on a Cyclone IV E series platform with the EP4CE15F23C8N FPGA as the primary chip. The FPGA implementation results align numerical simulations, confirming the practical applicability of the multibutterfly memristive chaotic circuit.</p></div>","PeriodicalId":792,"journal":{"name":"The European Physical Journal Plus","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Design and FPGA realization of memristive multibutterfly chaotic system featuring coexisting attractors and complex multistability behavior\",\"authors\":\"Minxiu Yan, Peng Du\",\"doi\":\"10.1140/epjp/s13360-024-05722-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Multibutterfly memristive chaotic systems (MMCSs) exhibit intricate multistable behavior and heightened randomness, making them highly advantageous for secure communications and image encryption. The paper provides a new five-dimensional chaotic system that incorporates two memristors into a 3D chaotic framework, leading to the creation of multibutterfly chaotic attractors. The quantity of multibutterfly chaotic attractors is capable of being managed by varying the parameters <span>\\\\(\\\\mathrm M\\\\)</span> and <span>\\\\(\\\\mathrm N\\\\)</span>. We conduct an in-depth analysis of the five-dimensional MMCS dynamics through methods like Lyapunov exponents, Poincare maps, phase diagrams, and bifurcation diagrams. We depicted the basin of attraction for exploring the system’s coexisting attractors. Furthermore, the five-dimensional MMCS exhibits the coexisting attractors through variations in the initial values. By tuning parameters <span>\\\\(k_{1}\\\\)</span> and <span>\\\\(k_{2}\\\\)</span>, the system’s amplitude can be adjusted. To validate the practical applicability of this system, we design a chaotic circuit based on the five-dimensional MMCS. The system is implemented on a Cyclone IV E series platform with the EP4CE15F23C8N FPGA as the primary chip. The FPGA implementation results align numerical simulations, confirming the practical applicability of the multibutterfly memristive chaotic circuit.</p></div>\",\"PeriodicalId\":792,\"journal\":{\"name\":\"The European Physical Journal Plus\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-10-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The European Physical Journal Plus\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1140/epjp/s13360-024-05722-x\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal Plus","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjp/s13360-024-05722-x","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
多蝶形忆阻器混沌系统(MMCS)表现出复杂的多稳态行为和更高的随机性,使其在安全通信和图像加密方面极具优势。本文提供了一种新的五维混沌系统,将两个忆阻器纳入三维混沌框架,从而产生了多蝶形混沌吸引子。多蝶形混沌吸引子的数量可以通过改变参数(\(\mathrm M\) 和 (\(\mathrm N\) )来管理。我们通过Lyapunov指数、Poincare图、相图和分岔图等方法对五维MMCS动力学进行了深入分析。我们描绘了吸引盆地,以探索系统的共存吸引子。此外,五维 MMCS 通过初始值的变化展示了共存吸引子。通过调整参数 \(k_{1}\) 和 \(k_{2}\),可以调整系统的振幅。为了验证该系统的实际应用性,我们设计了一个基于五维 MMCS 的混沌电路。该系统在 Cyclone IV E 系列平台上实现,主芯片为 EP4CE15F23C8N FPGA。FPGA 实现结果与数值仿真结果一致,证实了多蝶形忆阻式混沌电路的实用性。
Design and FPGA realization of memristive multibutterfly chaotic system featuring coexisting attractors and complex multistability behavior
Multibutterfly memristive chaotic systems (MMCSs) exhibit intricate multistable behavior and heightened randomness, making them highly advantageous for secure communications and image encryption. The paper provides a new five-dimensional chaotic system that incorporates two memristors into a 3D chaotic framework, leading to the creation of multibutterfly chaotic attractors. The quantity of multibutterfly chaotic attractors is capable of being managed by varying the parameters \(\mathrm M\) and \(\mathrm N\). We conduct an in-depth analysis of the five-dimensional MMCS dynamics through methods like Lyapunov exponents, Poincare maps, phase diagrams, and bifurcation diagrams. We depicted the basin of attraction for exploring the system’s coexisting attractors. Furthermore, the five-dimensional MMCS exhibits the coexisting attractors through variations in the initial values. By tuning parameters \(k_{1}\) and \(k_{2}\), the system’s amplitude can be adjusted. To validate the practical applicability of this system, we design a chaotic circuit based on the five-dimensional MMCS. The system is implemented on a Cyclone IV E series platform with the EP4CE15F23C8N FPGA as the primary chip. The FPGA implementation results align numerical simulations, confirming the practical applicability of the multibutterfly memristive chaotic circuit.
期刊介绍:
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