Variable-Fractional-Order Nosé–Hoover System: Chaotic Dynamics and Numerical Simulations - D. K. Almutairi; Dalal M. AlMutairi; Nidal E. Taha; Mohammed E. Dafaalla; Mohamed A. Abdoon (Fractal and Fractional)
This study explores the variable-order fractional Nosé–Hoover system, investigating the evolution of its chaotic and stable states under variable-order derivatives. Variable-order derivatives introduce greater complexity and adaptability into a system’s dynamics. The main objective is to examine these effects through numerical simulations, showcasing how changes in the order function influence a system’s behavior. The variable-order behavior is shown by phase space orbits and time series for various variable orders <semantics>α</semantics>. We look at how the system acts by using numerical solutions and numerical simulations. The phase space orbits and time series for different <semantics>α</semantics> show variable-order effects. The findings emphasize the role of variable-order derivatives in enhancing chaotic behavior, offering novel insights into their impact on dynamical systems.