A Novel Fractional‐Order Atmospheric Chaotic Model: Analysis, Fuzzy Control, and Circuit Realization

ABSTRACT A new three‐dimensional fractional‐order atmospheric model is proposed to describe the nonlinear interactions among temperature, wind, and humidity. The model extends the classical Lorenz‐type framework by incorporating fractional Caputo derivatives and nonlinear coupling terms, enabling a more realistic representation of memory‐dependent atmospheric processes. Theoretical analyses establish the existence, uniqueness, and boundedness of the model's solutions. The complex chaotic behavior exhibited by the system is confirmed through Lyapunov exponents, bifurcation analysis, the Kaplan‐Yorke dimension, and Poincaré map. Numerical simulations using the predictor‐corrector method demonstrate the transition from periodic to chaotic regimes as key parameters vary. A Mamdani‐type fuzzy logic controller (FLC) is designed to suppress chaotic behavior. Numerical results show that, under fuzzy control, chaotic oscillations are significantly reduced, and the system stabilizes approximately after 20 time units, indicating rapid convergence and effective chaos control. Synchronization between master and slave models is achieved via active control, offering potential applications in secure communication and atmospheric data integration. Furthermore, a Matlab Simulink‐based circuit is implemented to experimentally verify the theoretical and numerical findings. Sensitivity and global variance‐based analyses identify the most influential parameters governing the chaotic dynamics. The results confirm that fractional‐order dynamics and intelligent control can effectively regulate complex atmospheric behavior.