利用径向基函数神经网络对非线性变阶分数超混沌陈系统进行混沌分析

IF 3.1 3区 工程技术 Q2 NEUROSCIENCES
Sadam Hussain, Zia Bashir, M. G. Abbas Malik
{"title":"利用径向基函数神经网络对非线性变阶分数超混沌陈系统进行混沌分析","authors":"Sadam Hussain, Zia Bashir, M. G. Abbas Malik","doi":"10.1007/s11571-024-10118-9","DOIUrl":null,"url":null,"abstract":"<p>This research explores the various chaotic features of the hyperchaotic Chen dynamical system within a variable order fractional (VOF) calculus framework, employing an innovative approach with a nonlinear and adaptive radial basis function neural network. The study begins by computing the numerical solution of VOF differential equations for the hyperchaotic Chen system through a numerical scheme using the Caputo–Fabrizio derivative across a spectrum of different system control parameters. Subsequently, a comprehensive parametric model is formulated using RBFNN, considering the system’s various initial values. We systematically investigate the various chaotic attractors of the proposed system, employing statistical analysis, phase space reconstruction, and Lyapunov exponent. Additionally, we assess the effectiveness of the proposed computational RBFNN model using the Root Mean Square Error statistic. Importantly, the obtained results closely align with those derived from numerical algorithms, emphasizing the high accuracy and reliability of the designed network. The outcomes of this study have implications for studying chaos with variable fractional derivatives, with applications across various scientific and engineering domains. This work advances the understanding and applications of variable order fractional dynamics.</p>","PeriodicalId":10500,"journal":{"name":"Cognitive Neurodynamics","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Chaos analysis of nonlinear variable order fractional hyperchaotic Chen system utilizing radial basis function neural network\",\"authors\":\"Sadam Hussain, Zia Bashir, M. G. Abbas Malik\",\"doi\":\"10.1007/s11571-024-10118-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This research explores the various chaotic features of the hyperchaotic Chen dynamical system within a variable order fractional (VOF) calculus framework, employing an innovative approach with a nonlinear and adaptive radial basis function neural network. The study begins by computing the numerical solution of VOF differential equations for the hyperchaotic Chen system through a numerical scheme using the Caputo–Fabrizio derivative across a spectrum of different system control parameters. Subsequently, a comprehensive parametric model is formulated using RBFNN, considering the system’s various initial values. We systematically investigate the various chaotic attractors of the proposed system, employing statistical analysis, phase space reconstruction, and Lyapunov exponent. Additionally, we assess the effectiveness of the proposed computational RBFNN model using the Root Mean Square Error statistic. Importantly, the obtained results closely align with those derived from numerical algorithms, emphasizing the high accuracy and reliability of the designed network. The outcomes of this study have implications for studying chaos with variable fractional derivatives, with applications across various scientific and engineering domains. This work advances the understanding and applications of variable order fractional dynamics.</p>\",\"PeriodicalId\":10500,\"journal\":{\"name\":\"Cognitive Neurodynamics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.1000,\"publicationDate\":\"2024-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cognitive Neurodynamics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1007/s11571-024-10118-9\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"NEUROSCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cognitive Neurodynamics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s11571-024-10118-9","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"NEUROSCIENCES","Score":null,"Total":0}
引用次数: 0

摘要

本研究在变阶分数(VOF)微积分框架内,采用非线性和自适应径向基函数神经网络的创新方法,探索了超混沌陈氏动力系统的各种混沌特征。研究首先通过使用卡普托-法布里齐奥导数的数值方案,计算超混沌陈系统的 VOF 微分方程的数值解,并跨越不同的系统控制参数谱。随后,考虑到系统的各种初始值,使用 RBFNN 建立了一个综合参数模型。我们利用统计分析、相空间重构和 Lyapunov 指数,系统地研究了拟议系统的各种混沌吸引子。此外,我们还利用均方根误差统计量评估了所提出的 RBFNN 计算模型的有效性。重要的是,所获得的结果与数值算法得出的结果非常接近,强调了所设计网络的高准确性和可靠性。这项研究的成果对研究具有可变分数导数的混沌具有重要意义,可应用于各种科学和工程领域。这项工作推动了对变阶分数动力学的理解和应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Chaos analysis of nonlinear variable order fractional hyperchaotic Chen system utilizing radial basis function neural network

Chaos analysis of nonlinear variable order fractional hyperchaotic Chen system utilizing radial basis function neural network

This research explores the various chaotic features of the hyperchaotic Chen dynamical system within a variable order fractional (VOF) calculus framework, employing an innovative approach with a nonlinear and adaptive radial basis function neural network. The study begins by computing the numerical solution of VOF differential equations for the hyperchaotic Chen system through a numerical scheme using the Caputo–Fabrizio derivative across a spectrum of different system control parameters. Subsequently, a comprehensive parametric model is formulated using RBFNN, considering the system’s various initial values. We systematically investigate the various chaotic attractors of the proposed system, employing statistical analysis, phase space reconstruction, and Lyapunov exponent. Additionally, we assess the effectiveness of the proposed computational RBFNN model using the Root Mean Square Error statistic. Importantly, the obtained results closely align with those derived from numerical algorithms, emphasizing the high accuracy and reliability of the designed network. The outcomes of this study have implications for studying chaos with variable fractional derivatives, with applications across various scientific and engineering domains. This work advances the understanding and applications of variable order fractional dynamics.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Cognitive Neurodynamics
Cognitive Neurodynamics 医学-神经科学
CiteScore
6.90
自引率
18.90%
发文量
140
审稿时长
12 months
期刊介绍: Cognitive Neurodynamics provides a unique forum of communication and cooperation for scientists and engineers working in the field of cognitive neurodynamics, intelligent science and applications, bridging the gap between theory and application, without any preference for pure theoretical, experimental or computational models. The emphasis is to publish original models of cognitive neurodynamics, novel computational theories and experimental results. In particular, intelligent science inspired by cognitive neuroscience and neurodynamics is also very welcome. The scope of Cognitive Neurodynamics covers cognitive neuroscience, neural computation based on dynamics, computer science, intelligent science as well as their interdisciplinary applications in the natural and engineering sciences. Papers that are appropriate for non-specialist readers are encouraged. 1. There is no page limit for manuscripts submitted to Cognitive Neurodynamics. Research papers should clearly represent an important advance of especially broad interest to researchers and technologists in neuroscience, biophysics, BCI, neural computer and intelligent robotics. 2. Cognitive Neurodynamics also welcomes brief communications: short papers reporting results that are of genuinely broad interest but that for one reason and another do not make a sufficiently complete story to justify a full article publication. Brief Communications should consist of approximately four manuscript pages. 3. Cognitive Neurodynamics publishes review articles in which a specific field is reviewed through an exhaustive literature survey. There are no restrictions on the number of pages. Review articles are usually invited, but submitted reviews will also be considered.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信