Modeling nonlinear variable-order fractional chaotic systems using the Caputo-Fabrizio operator and radial basis...

Area of Science:

• Nonlinear Dynamics
• Fractional Calculus
• Computational Intelligence

Background:

• Traditional fractional chaotic models often use constant fractional orders, limiting their ability to represent evolving system memory.
• Real-world dynamic systems exhibit complex behaviors that necessitate more adaptable modeling approaches.

Purpose of the Study:

• To investigate the characteristics of a nonlinear fractional chaotic model using a variable fractional-order approach.
• To enhance the accuracy and realism of chaotic behavior representation for dynamic applications.
• To leverage radial basis function neural networks (RBFNN) for efficient modeling and prediction.

Main Methods:

• Employed the Caputo-Fabrizio fractional derivative to describe system dynamics.
• Utilized radial basis function neural networks (RBFNN) for learning and prediction.
• Incorporated variable fractional derivatives to allow evolving memory effects.
• Performed phase space reconstruction to analyze system evolution across different fractional orders.

Main Results:

• The variable fractional-order model demonstrated superior flexibility and precision compared to fixed-order models.
• Achieved a minimal error threshold below [Formula: see text], confirming model reliability and robustness.
• RBFNN provided efficient prediction of complex chaotic behavior with reduced computational cost.

Conclusions:

• Variable fractional-order modeling offers enhanced accuracy and realism for nonlinear chaotic systems.
• The proposed framework is efficient and provides a novel approach for studying and predicting chaotic dynamics.
• Potential applications include secure communication, control systems, and signal processing.