Dynamical Analysis and Backstepping-Based Synchronization of a Fractional-Order Hyperchaotic Yan System Using RBF Neural Networks

Abstract

This paper explores the dynamic behavior and control of a novel 4D fractional-order hyperchaotic Yan system, characterized by transitions between stability, periodicity, and chaos, driven by fractional-order parameters and initial conditions. The system’s complex nonlinear dynamics are comprehensively analyzed using phase portraits, bifurcation diagrams, Lyapunov exponents, Poincaré maps, and the 0–1 test, revealing a broad spectrum of behaviors influenced by variations in system parameters and fractional-order effects. A robust backstepping control strategy is implemented to achieve synchronization and ensure system stability. Additionally, a radial basis function neural network (RBFNN) is used to model the system dynamics with high accuracy, as shown by a minimal root mean square error. This study presents an innovative approach that combines data-driven modeling with the Yan system, offering enhanced insights into their intricate dynamics. The results align closely with numerical solutions based on the Caputo derivative, underscoring the accuracy and reliability of the RBFNN methodology.