• 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

一个具有不同族隐藏和自激吸引子的新型分数阶混沌系统。

A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors.

作者信息

Munoz-Pacheco Jesus M, Zambrano-Serrano Ernesto, Volos Christos, Jafari Sajad, Kengne Jacques, Rajagopal Karthikeyan

机构信息

Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72000, Mexico.

Department of Physics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece.

出版信息

Entropy (Basel). 2018 Jul 28;20(8):564. doi: 10.3390/e20080564.

DOI:10.3390/e20080564
PMID:33265653
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7513089/
Abstract

In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-excited chaotic attractors, the system has four spiral-saddle-type equilibrium points, or two nonhyperbolic equilibria. Besides, for a certain value of the parameter, a fractional-order no-equilibrium system is obtained. This no-equilibrium system presents a hidden chaotic attractor with a `hurricane'-like shape in the phase space. Multistability is also observed, since a hidden chaotic attractor coexists with a periodic one. The chaos generation in the new fractional-order system is demonstrated by the Lyapunov exponents method and equilibrium stability. Moreover, the complexity of the self-excited and hidden chaotic attractors is analyzed by computing their spectral entropy and Brownian-like motions. Finally, a pseudo-random number generator is designed using the hidden dynamics.

摘要

在这项工作中，引入了一个具有单个参数和四个非线性项的新型分数阶混沌系统。一个显著特征是，通过改变系统参数，分数阶系统会产生几种复杂的动力学：自激吸引子、隐藏吸引子以及隐藏吸引子的共存。在自激混沌吸引子族中，系统有四个螺旋鞍型平衡点，或者两个非双曲平衡点。此外，对于参数的某个值，可得到一个分数阶无平衡点系统。这个无平衡点系统在相空间中呈现出一个具有“飓风”形状的隐藏混沌吸引子。还观察到了多稳定性，因为一个隐藏混沌吸引子与一个周期吸引子共存。通过李雅普诺夫指数方法和平衡稳定性证明了新分数阶系统中的混沌产生。此外，通过计算自激和隐藏混沌吸引子的谱熵以及类布朗运动来分析它们的复杂性。最后，利用隐藏动力学设计了一个伪随机数发生器。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/e9e0e0638efe/entropy-20-00564-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/7a3247244e3d/entropy-20-00564-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/55d22d14bc6c/entropy-20-00564-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/ae9f3df3c006/entropy-20-00564-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/64aef5b4d232/entropy-20-00564-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/aac235ea9d59/entropy-20-00564-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/c4f63708143e/entropy-20-00564-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/864ee4ec9a2a/entropy-20-00564-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/c6b56b5e2742/entropy-20-00564-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/3ab8b8704c47/entropy-20-00564-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/b08a7aedac0f/entropy-20-00564-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/00cc58d89e5e/entropy-20-00564-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/e9e0e0638efe/entropy-20-00564-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/7a3247244e3d/entropy-20-00564-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/55d22d14bc6c/entropy-20-00564-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/ae9f3df3c006/entropy-20-00564-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/64aef5b4d232/entropy-20-00564-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/aac235ea9d59/entropy-20-00564-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/c4f63708143e/entropy-20-00564-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/864ee4ec9a2a/entropy-20-00564-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/c6b56b5e2742/entropy-20-00564-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/3ab8b8704c47/entropy-20-00564-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/b08a7aedac0f/entropy-20-00564-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/00cc58d89e5e/entropy-20-00564-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5cd9/7513089/e9e0e0638efe/entropy-20-00564-g012.jpg

相似文献

1
A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors.一个具有不同族隐藏和自激吸引子的新型分数阶混沌系统。
Entropy (Basel). 2018 Jul 28;20(8):564. doi: 10.3390/e20080564.
2
Chaotic attractors that exist only in fractional-order case.只存在于分数阶情况下的混沌吸引子。
J Adv Res. 2023 Mar;45:183-192. doi: 10.1016/j.jare.2022.03.008. Epub 2022 Mar 21.
3
Dynamics and Entropy Analysis for a New 4-D Hyperchaotic System with Coexisting Hidden Attractors.具有共存隐藏吸引子的新型四维超混沌系统的动力学与熵分析
Entropy (Basel). 2019 Mar 15;21(3):287. doi: 10.3390/e21030287.
4
Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function.具有非单调激活函数的惯性神经网络中周期轨道和混沌吸引子的混合共存。
Math Biosci Eng. 2019 Jul 11;16(6):6406-6425. doi: 10.3934/mbe.2019320.
5
Analysis and circuit implementation of a non-equilibrium fractional-order chaotic system with hidden multistability and special offset-boosting.非平衡分数阶混沌系统的分析与电路实现，具有隐藏多稳性和特殊的偏置增强。
Chaos. 2023 Mar;33(3):033107. doi: 10.1063/5.0130083.
6
Hidden hyperchaotic attractors in a new 4D fractional order system and its synchronization.一个新的四维分数阶系统中的隐藏超混沌吸引子及其同步
Chaos. 2020 Mar;30(3):033129. doi: 10.1063/1.5136057.
7
Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems.通过新的可公度和不可公度非平衡分数阶混沌系统生成多向可变隐藏吸引子
Entropy (Basel). 2021 Feb 24;23(3):261. doi: 10.3390/e23030261.
8
Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability.在具有极端多稳定性的新型4D非平衡混沌系统中生成一到四翼隐藏吸引子。
Chaos. 2018 Jan;28(1):013113. doi: 10.1063/1.5006214.
9
Coexisting hidden and self-excited attractors in a locally active memristor-based circuit.基于局部有源忆阻器的电路中并存的隐藏吸引子和自激吸引子。
Chaos. 2020 Oct;30(10):103123. doi: 10.1063/5.0002061.
10
Bistability and hidden attractors in the paradigmatic Rössler'76 system.典型的罗斯勒'76系统中的双稳性和隐藏吸引子。
Chaos. 2020 Dec;30(12):123144. doi: 10.1063/5.0030023.

引用本文的文献

1
A new buffering theory of social support and psychological stress.一种新的社会支持和心理压力的缓冲理论。
PLoS One. 2022 Oct 12;17(10):e0275364. doi: 10.1371/journal.pone.0275364. eCollection 2022.
2
A Hidden Chaotic System with Multiple Attractors.一个具有多个吸引子的隐藏混沌系统。
Entropy (Basel). 2021 Oct 14;23(10):1341. doi: 10.3390/e23101341.
3
Adaptive Synchronization Strategy between Two Autonomous Dissipative Chaotic Systems Using Fractional-Order Mittag-Leffler Stability.基于分数阶米塔格-莱夫勒稳定性的两个自治耗散混沌系统的自适应同步策略

本文引用的文献

1
Complex Systems and Fractional Dynamics.复杂系统与分数动力学
Entropy (Basel). 2018 Jul 3;20(7):507. doi: 10.3390/e20070507.
2
A New Two-Dimensional Map with Hidden Attractors.一种具有隐藏吸引子的新型二维映射。
Entropy (Basel). 2018 Apr 27;20(5):322. doi: 10.3390/e20050322.
3
A New Chaotic System with Multiple Attractors: Dynamic Analysis, Circuit Realization and S-Box Design.一种具有多个吸引子的新型混沌系统：动态分析、电路实现与S盒设计
Entropy (Basel). 2019 Apr 10;21(4):383. doi: 10.3390/e21040383.
4
Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors.具有隐藏吸引子和自激吸引子的复杂系统的非线性动力学与熵
Entropy (Basel). 2019 Apr 5;21(4):370. doi: 10.3390/e21040370.
5
Dynamics and Entropy Analysis for a New 4-D Hyperchaotic System with Coexisting Hidden Attractors.具有共存隐藏吸引子的新型四维超混沌系统的动力学与熵分析
Entropy (Basel). 2019 Mar 15;21(3):287. doi: 10.3390/e21030287.
6
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.
7
Dynamics and Complexity of a New 4D Chaotic Laser System.一种新型四维混沌激光系统的动力学与复杂性
Entropy (Basel). 2019 Jan 7;21(1):34. doi: 10.3390/e21010034.
8
Parameter Identification of Fractional-Order Discrete Chaotic Systems.分数阶离散混沌系统的参数辨识
Entropy (Basel). 2019 Jan 1;21(1):27. doi: 10.3390/e21010027.
9
Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization.具有时滞的新型分数阶Hopfield神经网络的动力学分析及其广义投影同步
Entropy (Basel). 2018 Dec 20;21(1):1. doi: 10.3390/e21010001.
10
Approximation to Hadamard Derivative via the Finite Part Integral.通过有限部分积分逼近哈达玛导数
Entropy (Basel). 2018 Dec 18;20(12):983. doi: 10.3390/e20120983.
Entropy (Basel). 2017 Dec 27;20(1):12. doi: 10.3390/e20010012.
4
Comments on "Coexistence of hidden chaotic attractors in a novel no-equilibrium system" (Nonlinear Dyn, doi:10.1007/s11071-016-3170-x).对《一个新型非平衡系统中隐藏混沌吸引子的共存》的评论（《非线性动力学》，doi:10.1007/s11071-016-3170-x）
Nonlinear Dyn. 2017;90(1):749-754. doi: 10.1007/s11071-017-3671-2. Epub 2017 Jul 18.
5
Generation of multi-scroll attractors without equilibria via piecewise linear systems.通过分段线性系统生成无平衡点的多涡卷吸引子。
Chaos. 2017 May;27(5):053109. doi: 10.1063/1.4983523.
6
Classifying and quantifying basins of attraction.吸引子盆地的分类与量化。
Chaos. 2015 Aug;25(8):083101. doi: 10.1063/1.4927643.
7
Design of multidirectional multiscroll chaotic attractors based on fractional differential systems via switching control.基于分数阶微分系统通过切换控制设计多向多涡卷混沌吸引子
Chaos. 2006 Dec;16(4):043120. doi: 10.1063/1.2401061.