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

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  author =       "Fei Gao and Teng Lee and Wen-Jing Cao and 
                 Xue-jing Lee and Yan-fang Deng and Heng-qing Tong",
  title =        "Self-evolution of hyper fractional order chaos driven
                 by a novel approach through genetic programming",
  journal =      "Expert Systems with Applications",
  year =         "2016",
  volume =       "52",
  pages =        "1--15",
  month =        "15 " # jun # " 2016",
  keywords =     "genetic algorithms, genetic programming,
                 Fractional-order chaos, Self-evolution, United
                 functional extrema model",
  ISSN =         "0957-4174",
  DOI =          "doi:10.1016/j.eswa.2015.12.033",
  size =         "15 pages",
  abstract =     "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.",
  notes =        "Department of Mathematics, School of Science, Wuhan
                 University of Technology, Luoshi Road 122, Wuhan, Hubei
                 430070, China.

                 Signal Processing Group, Department of Electronics and
                 Telecommunications, Norwegian University of Science and
                 Technology, Trondheim N-7491, Norway",

Genetic Programming entries for Fei Gao Teng Lee Wen-Jing Cao Xue-jing Lee Yan-fang Deng Heng-qing Tong