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Chaos analysis of nonlinear variable order fractional hyperchaotic Chen system utilizing radial basis function neural
Sadam Hussain1, Zia Bashir1, M G Abbas Malik2
1Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320 Pakistan.
Cognitive Neurodynamics
|December 16, 2024
Summary
This study investigates chaotic dynamics in a hyperchaotic Chen system using variable order fractional calculus and a radial basis function neural network (RBFNN). The RBFNN accurately models chaotic behavior, advancing fractional dynamics research.
Area of Science:
- Nonlinear Dynamics
- Fractional Calculus
- Computational Intelligence
Background:
- The hyperchaotic Chen system exhibits complex dynamics.
- Fractional calculus offers a more generalized framework for modeling dynamical systems.
- Radial Basis Function Neural Networks (RBFNN) are powerful tools for approximating complex functions.
Purpose of the Study:
- To explore chaotic features of the hyperchaotic Chen system within a variable order fractional (VOF) calculus framework.
- To develop and validate a nonlinear and adaptive RBFNN for modeling VOF chaotic systems.
- To investigate the system's chaotic attractors and assess the RBFNN's accuracy.
Main Methods:
- Numerical computation of VOF differential equations using the Caputo-Fabrizio derivative.
- Formulation of a parametric RBFNN model for the hyperchaotic Chen system.
- Analysis of chaotic attractors using statistical methods, phase space reconstruction, and Lyapunov exponents.
- Validation of the RBFNN model using Root Mean Square Error (RMSE).
Main Results:
- The study successfully computed numerical solutions for the VOF hyperchaotic Chen system.
- A comprehensive parametric RBFNN model was developed and validated.
- Chaotic attractors were systematically investigated, revealing complex dynamics.
- The RBFNN demonstrated high accuracy and reliability, with results closely matching numerical algorithms.
Conclusions:
- The proposed RBFNN approach is effective for studying chaos in VOF systems.
- This research advances the understanding and application of variable order fractional dynamics.
- The findings have potential implications for various scientific and engineering fields involving chaotic systems.
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