{"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}
引用次数: 0
Abstract
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.
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.