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

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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.

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Acknowledgements

We are grateful to the editor and anonymous reviewers for reviewing the manuscript and providing constructive comments for improvement. The authors would like to thank Prince Sultan University for their support.

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan

    Sadam Hussain & Zia Bashir

  2. College of Computer and Information Science, Prince Sultan University, Riyadh, Saudi Arabia

    M. G. Abbas Malik

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  1. Sadam Hussain
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  2. Zia Bashir
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Correspondence to Zia Bashir.

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Hussain, S., Bashir, Z. & Malik, M.G.A. Chaos analysis of nonlinear variable order fractional hyperchaotic Chen system utilizing radial basis function neural network. Cogn Neurodyn (2024). https://doi.org/10.1007/s11571-024-10118-9

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  • DOI: https://doi.org/10.1007/s11571-024-10118-9

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