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Enhanced global flower pollination algorithm for parameter identification of chaotic and hyper-chaotic system

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Abstract

The problem of system parameter identification is a fundamental problem in the field of nonlinear science, which can be described as a multidimensional optimization problem. In this paper, an enhanced global flower pollination algorithm (GFPA) is proposed for parameter identification of chaotic and hyper-chaotic systems. The motion trajectory of the flower pollination algorithm is analyzed for the first time, and the equation of the algorithm exploration phase is improved by the chaotic mapping method to ensure the convergence of the algorithm in the exploration phase. In addition, in order to improve the convergence speed of the algorithm, the update method of the exploitation phase is reset by using the best information to guide the searching. Through analysis, the proposed new algorithm can guarantee the convergence of the algorithm without increasing the time complexity. Finally, we identify and validate the system of the Lorenz, Rössler, Chen and the system of the Rössler hyper-chaotic, Chen hyper-chaotic. The experimental results show that GFPA has better identification effect.

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Abbreviations

X :

State vector of the system

\(\dot{X}\) :

A n-dimensional chaotic system

\(\tilde{X}\) :

State vector of the system to be identified

\(\tilde{\dot{X}}\) :

The system to be identified

\(X_0\) :

Initial state vector of the system

\(\theta _0\) :

Actual sequence of parameters

\(\theta \) :

Estimate value for the system identification

M :

Length of the output sequence obtained from the operation of the real chaotic system

x :

Decision variables in optimization algorithms

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Funding

This work was supported by Nation Natural Science Foundation of China (U1433116), the Fundamental Research Funds for the Central Universities (NZ2013306) and Science and Technology Research Project of Jiangxi Education Department (GJJ180442)

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Authors and Affiliations

  1. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Yang Chen & DeChang Pi

  2. Computer Science and Engineering, Southeast University, Nanjing, 211189, China

    Bi Wang

Authors
  1. Yang Chen
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  2. DeChang Pi
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  3. Bi Wang
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Correspondence to DeChang Pi.

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Chen, Y., Pi, D. & Wang, B. Enhanced global flower pollination algorithm for parameter identification of chaotic and hyper-chaotic system. Nonlinear Dyn 97, 1343–1358 (2019). https://doi.org/10.1007/s11071-019-05052-z

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  • DOI: https://doi.org/10.1007/s11071-019-05052-z

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