<p>This article introduces a novel hyperchaotic system conceived in the Caputo fractional derivative framework. The proposed system exhibits a multi-scroll attractor, demonstrating a higher degree of complexity and richer dynamics compared to conventional chaotic and hyperchaotic systems. A thorough investigation into the system’s dynamical properties is conducted, encompassing analyses of dissipativity, stability, and Hopf bifurcation. Numerical simulations are carried out to highlight the significant influence of system parameters on the dynamic characteristics, as evidenced by Kaplan–Yorke dimension, bifurcation diagrams, time series plots, and phase portraits. Notably, the Lyapunov exponent spectrum is plotted to confirm the system’s hyperchaotic behavior that is its sensitivity to initial conditions. Furthermore, the study exploits the active control method to achieve control and synchronization of the hyperchaotic system. The results demonstrate that the considered control method ensures a rapid and robust complete synchronization and anti-synchronization.</p>

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On the dynamics and synchronization of a new fractional-order hyperchaotic system

  • A. Sai Lekshmi,
  • V. Balakumar,
  • Donato Cafagna

摘要

This article introduces a novel hyperchaotic system conceived in the Caputo fractional derivative framework. The proposed system exhibits a multi-scroll attractor, demonstrating a higher degree of complexity and richer dynamics compared to conventional chaotic and hyperchaotic systems. A thorough investigation into the system’s dynamical properties is conducted, encompassing analyses of dissipativity, stability, and Hopf bifurcation. Numerical simulations are carried out to highlight the significant influence of system parameters on the dynamic characteristics, as evidenced by Kaplan–Yorke dimension, bifurcation diagrams, time series plots, and phase portraits. Notably, the Lyapunov exponent spectrum is plotted to confirm the system’s hyperchaotic behavior that is its sensitivity to initial conditions. Furthermore, the study exploits the active control method to achieve control and synchronization of the hyperchaotic system. The results demonstrate that the considered control method ensures a rapid and robust complete synchronization and anti-synchronization.