• 文献检索
  • 文档翻译
  • 深度研究
  • 学术资讯
  • Suppr Zotero 插件Zotero 插件
  • 邀请有礼
  • 套餐&价格
  • 历史记录
应用&插件
Suppr Zotero 插件Zotero 插件浏览器插件Mac 客户端Windows 客户端微信小程序
定价
高级版会员购买积分包购买API积分包
服务
文献检索文档翻译深度研究API 文档MCP 服务
关于我们
关于 Suppr公司介绍联系我们用户协议隐私条款
关注我们

Suppr 超能文献

核心技术专利：CN118964589B侵权必究
粤ICP备2023148730 号-1Suppr @ 2026

文献检索

告别复杂PubMed语法，用中文像聊天一样搜索，搜遍4000万医学文献。AI智能推荐，让科研检索更轻松。

立即免费搜索

文件翻译

保留排版，准确专业，支持PDF/Word/PPT等文件格式，支持 12+语言互译。

免费翻译文档

深度研究

AI帮你快速写综述，25分钟生成高质量综述，智能提取关键信息，辅助科研写作。

立即免费体验

基于高阶振荡方程的混沌系统。

Chaotic systems based on higher-order oscillatory equations.

作者信息

Petrzela Jiri

机构信息

Department of Radio Electronics, Brno University of Technology, Brno, 61600, Czech Republic.

Department of Electrical Engineering, University of Defence, Brno, 66210, Czech Republic.

出版信息

Sci Rep. 2024 Sep 10;14(1):21075. doi: 10.1038/s41598-024-72034-6.

DOI:10.1038/s41598-024-72034-6
PMID:39256452
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11387476/
Abstract

This paper discusses the design process toward new lumped chaotic systems that originates in higher-order ordinary differential equations commonly used as description of ideal oscillators. In investigated third-order case, two chaotic oscillators were constructed. These systems are dual in the sense of vector field geometry local to fixed points. The existence of robust chaos was proved by both standard routines of numerical analysis and practical measurement. For the fourth-order oscillatory equation, the concept based on interaction between superinductor and supercapacitor was examined in detail. Since both "superelements" are active, the nonlinearity essential to the evolution of chaos is fully passive. It is demonstrated that complex motion is robust and does not represent long transient behavior or numerical artefact. The existence of chaos was verified using standard quantifiers of the flow, such as the largest Lyapunov exponents, recurrence plots, approximate entropy and sensitivity calculation. A good final agreement between theoretical assumptions and practical results will be concluded, on a visual comparison basis.

摘要

本文讨论了源自高阶常微分方程的新型集总混沌系统的设计过程，这些方程通常用于描述理想振荡器。在研究的三阶情况下，构建了两个混沌振荡器。从定点局部的向量场几何意义上讲，这些系统是对偶的。通过数值分析的标准程序和实际测量都证明了鲁棒混沌的存在。对于四阶振荡方程，详细研究了基于超级电感和超级电容相互作用的概念。由于两个“超元件”都是有源的，混沌演化所必需的非线性是完全无源的。结果表明，复杂运动是鲁棒的，并不代表长时间的瞬态行为或数值假象。使用流的标准量化指标，如最大Lyapunov指数、递归图、近似熵和灵敏度计算，验证了混沌的存在。在视觉比较的基础上，理论假设和实际结果将得出良好的最终一致性。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/92ad745062f0/41598_2024_72034_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/d6273b03ecb7/41598_2024_72034_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/62b759c32a76/41598_2024_72034_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/3ab9f33a4217/41598_2024_72034_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/2fa5766cccdd/41598_2024_72034_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/ad068855082c/41598_2024_72034_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/5f940d600714/41598_2024_72034_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/e6897fd57f07/41598_2024_72034_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/293d1eb4f10c/41598_2024_72034_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/92ad745062f0/41598_2024_72034_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/d6273b03ecb7/41598_2024_72034_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/62b759c32a76/41598_2024_72034_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/3ab9f33a4217/41598_2024_72034_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/2fa5766cccdd/41598_2024_72034_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/ad068855082c/41598_2024_72034_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/5f940d600714/41598_2024_72034_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/e6897fd57f07/41598_2024_72034_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/293d1eb4f10c/41598_2024_72034_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/395e/11387476/92ad745062f0/41598_2024_72034_Fig9_HTML.jpg

相似文献

1
Chaotic systems based on higher-order oscillatory equations.基于高阶振荡方程的混沌系统。
Sci Rep. 2024 Sep 10;14(1):21075. doi: 10.1038/s41598-024-72034-6.
2
Using Lyapunov exponents to predict the onset of chaos in nonlinear oscillators.利用李雅普诺夫指数预测非线性振荡器中的混沌起始。
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Jul;66(1 Pt 2):016214. doi: 10.1103/PhysRevE.66.016214. Epub 2002 Jul 25.
3
Experimental evidence of deterministic coherence resonance in coupled chaotic systems with frequency mismatch.频率失配的耦合混沌系统中确定性相干共振的实验证据。
Phys Rev E. 2016 Jul;94(1-1):012218. doi: 10.1103/PhysRevE.94.012218. Epub 2016 Jul 15.
4
An Approach for the Generation of an Nth-Order Chaotic System with Hyperbolic Sine.一种基于双曲正弦生成N阶混沌系统的方法。
Entropy (Basel). 2018 Mar 27;20(4):230. doi: 10.3390/e20040230.
5
An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps.扩展熵混沌度的一种改进计算公式及其在二维混沌映射中的应用
Entropy (Basel). 2021 Nov 14;23(11):1511. doi: 10.3390/e23111511.
6
On the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum.关于具有平坦功率谱的自主席尔瓦 - 杨型混沌振荡器的建模与非线性动力学
Chaos. 2014 Dec;24(4):043134. doi: 10.1063/1.4903313.
7
Chaotic Map with No Fixed Points: Entropy, Implementation and Control.无不动点的混沌映射：熵、实现与控制
Entropy (Basel). 2019 Mar 14;21(3):279. doi: 10.3390/e21030279.
8
Dynamical invariants and inverse period-doubling cascades in multi-delay systems.多延迟系统中的动力学不变量与逆倍周期分岔级联
Chaos. 2021 Oct;31(10):103129. doi: 10.1063/5.0056097.
9
The frustrated and compositional nature of chaos in small Hopfield networks.小霍普菲尔德网络中混沌的受挫与组合性质。
Neural Netw. 1998 Aug;11(6):1017-1025. doi: 10.1016/s0893-6080(98)00056-2.
10
Chaotic nature of the electroencephalogram during shallow and deep anesthesia: From analysis of the Lyapunov exponent.脑电图在浅麻醉和深麻醉期间的混沌特性：来自李雅普诺夫指数的分析。
Neuroscience. 2024 Oct 4;557:116-123. doi: 10.1016/j.neuroscience.2024.08.016. Epub 2024 Aug 13.

引用本文的文献

1
Chaos-enhanced manganese electrolysis: nodule suppression and improved efficiency using controllable chaotic electrical signals.混沌增强型锰电解：利用可控混沌电信号抑制结瘤并提高效率
Sci Rep. 2025 Jan 2;15(1):59. doi: 10.1038/s41598-024-83747-z.

本文引用的文献

1
Dynamical behaviors, circuit design, and synchronization of a novel symmetric chaotic system with coexisting attractors.新型对称混沌系统共存吸引子的动力学行为、电路设计与同步。
Sci Rep. 2023 Feb 2;13(1):1893. doi: 10.1038/s41598-023-28509-z.
2
Fractional-Order Chaotic Memory with Wideband Constant Phase Elements.具有宽带恒定相位元件的分数阶混沌存储器。
Entropy (Basel). 2020 Apr 9;22(4):422. doi: 10.3390/e22040422.
3
Approximate Entropy and Sample Entropy: A Comprehensive Tutorial.近似熵与样本熵：全面教程
Entropy (Basel). 2019 May 28;21(6):541. doi: 10.3390/e21060541.
4
Strange Attractors Generated by Multiple-Valued Static Memory Cell with Polynomial Approximation of Resonant Tunneling Diodes.由具有共振隧穿二极管多项式逼近的多值静态存储单元生成的奇怪吸引子。
Entropy (Basel). 2018 Sep 12;20(9):697. doi: 10.3390/e20090697.
5
On the dynamics of a simplified canonical Chua's oscillator with smooth hyperbolic sine nonlinearity: Hyperchaos, multistability and multistability control.具有光滑双曲正弦非线性的简化规范蔡氏振荡器的动力学：超混沌、多稳定性和多稳定性控制。
Chaos. 2019 Nov;29(11):113105. doi: 10.1063/1.5121028.
6
Identification of minimal parameters for optimal suppression of chaos in dissipative driven systems.识别用于最优抑制耗散驱动系统中混沌现象的最小参数。
Sci Rep. 2017 Dec 21;7(1):17988. doi: 10.1038/s41598-017-17969-9.