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<p>This study analyzes the dynamics of a novel variable order hyper-chaotic Lü system, employing a nonlinear radial basis function neural network (RBFNN) structure. We compute the physical parameters of this intricate system using a variable order fractional Caputo-Fabrizio numerical scheme, considering diverse stochastic control scenarios. Subsequently, we model the system’s behavior with RBFNN under various initial conditions, analyzing multiple chaotic manifestations through Lyapunov exponents. Phase diagrams illustrate the system’s compact dynamical behavior, indicating potential real-world applications. We evaluate the suitability of the time delay chaotic pattern within the variable order fractional domain using the average mutual information technique, considering fluctuations influenced by numerical algorithms and time step sizes. Our proposed RBFNN design demonstrates exceptional effectiveness for soft computing and dynamic analysis of chaotic systems within the variable order fractional domain.</p>

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Modeling and analysis of variable fractional order hyper-chaotic Lü system with radial basis function neural networks

  • 期刊论文

  • 发表日期：

    2025年7月31日

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  • Muhammad Waseem Akhtar,
  • Zia Bashir,
  • M. G. Abbas Malik

摘要

This study analyzes the dynamics of a novel variable order hyper-chaotic Lü system, employing a nonlinear radial basis function neural network (RBFNN) structure. We compute the physical parameters of this intricate system using a variable order fractional Caputo-Fabrizio numerical scheme, considering diverse stochastic control scenarios. Subsequently, we model the system’s behavior with RBFNN under various initial conditions, analyzing multiple chaotic manifestations through Lyapunov exponents. Phase diagrams illustrate the system’s compact dynamical behavior, indicating potential real-world applications. We evaluate the suitability of the time delay chaotic pattern within the variable order fractional domain using the average mutual information technique, considering fluctuations influenced by numerical algorithms and time step sizes. Our proposed RBFNN design demonstrates exceptional effectiveness for soft computing and dynamic analysis of chaotic systems within the variable order fractional domain.