Fractional-Order Unified Chaotic System Implementation

This article demonstrates the implementation methodology of a fractional-order unified chaotic system. The system realization establishes fundamental groundwork for applying fractional-order chaotic systems in practical scenarios. Fractional-order chaotic systems represent a crucial concept with significant problem-solving capabilities in domains such as financial market prediction and image processing. The implementation employs numerical algorithms like the Grünwald-Letnikov or Caputo definition for fractional calculus, coupled with Runge-Kutta methods for system integration. Key functions include parameter initialization for unified chaotic system dynamics (typically controlled via a single parameter spanning Lorenz, Lü, and Chen systems) and fractional-order configuration through transfer function approximations or direct numerical differentiation. This program's development holds substantial importance for advancing fractional-order chaotic system applications across diverse fields. Furthermore, the system warrants continued investigation to uncover additional potential applications and refine its theoretical framework through enhanced stability analysis and optimization techniques.