Self-evolution of hyper fractional order chaos driven by a novel approach through genetic programming

• Fractional order chaos (FOC) evolution.
• United functional extrema model (UFEM).
• Self-evolution for FOC.
• Driven by Genetic programming through reconstruction.

To find best inherent chaotic systems behind the complex phenomena is of vital important in Complexity science research. In this paper, a novel non-Lyapunov methodology is proposed to self-evolve the best hyper fractional order chaos automatically driven by a computational intelligent method, genetic programming. Rather than the unknown systematic parameters and fractional orders, the expressions of fractional-order differential equations (FODE) are taken as particular independent variables of a proper converted non-negative minimization of special functional extrema in the proposed united functional extrema model (UFEM), then it is free of the hypotheses that the definite forms of FODE are given but some parameters and fractional orders unknown. To demonstrate the potential of the proposed methodology, simulations are done to evolve a series of benchmark hyper and normal fractional chaotic systems in complexity science. The experiments’ results show that the proposed paradigm of fractional order chaos driven by genetic programming is a successful method for chaos’ automatic self-evolution, with the advantages of high precision and robustness.