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Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional‐Order Chaotic Systems

Author

Listed:
  • Fei Gao
  • Xue-Jing Lee
  • Heng-qing Tong
  • Feng-xia Fei
  • Hua-ling Zhao

Abstract

In this paper, a non‐Lyapunov novel approach is proposed to estimate the unknown parameters and orders together for noncommensurate and hyper fractional chaotic systems based on cuckoo search oriented statistically by the differential evolution (CSODE). Firstly, a novel Gaos’ mathematical model is proposed and analyzed in three submodels, not only for the unknown orders and parameters’ identification but also for systems’ reconstruction of fractional chaos systems with time delays or not. Then the problems of fractional‐order chaos’ identification are converted into a multiple modal nonnegative functions’ minimization through a proper translation, which takes fractional‐orders and parameters as its particular independent variables. And the objective is to find the best combinations of fractional‐orders and systematic parameters of fractional order chaotic systems as special independent variables such that the objective function is minimized. Simulations are done to estimate a series of noncommensurate and hyper fractional chaotic systems with the new approaches based on CSODE, the cuckoo search, and Genetic Algorithm, respectively. The experiments’ results show that the proposed identification mechanism based on CSODE for fractional orders and parameters is a successful method for fractional‐order chaotic systems, with the advantages of high precision and robustness.

Suggested Citation

  • Fei Gao & Xue-Jing Lee & Heng-qing Tong & Feng-xia Fei & Hua-ling Zhao, 2013. "Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional‐Order Chaotic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:382834
    DOI: 10.1155/2013/382834
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    References listed on IDEAS

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    Cited by:

    1. A. H. Bhrawy & M. A. Alghamdi, 2014. "A Shifted Jacobi‐Gauss Collocation Scheme for Solving Fractional Neutral Functional‐Differential Equations," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    2. Ali H. Bhrawy & Abdulrahim AlZahrani & Dumitru Baleanu & Yahia Alhamed, 2014. "A Modified Generalized Laguerre‐Gauss Collocation Method for Fractional Neutral Functional‐Differential Equations on the Half‐Line," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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