Nonlinear Dynamics

, Volume 95, Issue 3, pp 2491–2542 | Cite as

Parameter identification of fractional-order chaotic systems using different Meta-heuristic Optimization Algorithms

  • D. A. Yousri
  • Amr M. AbdelAty
  • Lobna A. SaidEmail author
  • A. S. Elwakil
  • Brent Maundy
  • Ahmed G. Radwan
Original Paper


Fractional-order chaotic systems (FOCS) parameter identification is an essential issue in chaos control and synchronization process. In this paper, different recent Meta-heuristic Optimization Algorithms are used to estimate the parameters and orders of three FOCS. The investigated systems are Arneodo, Borah rotational attractor and Chen double- and four-wing systems. The employed algorithms are the Salp Swarm Algorithm, Whale Optimization Algorithm, Moth-Flame Optimizer, Grey Wolf Optimizer and the Flower Pollination Algorithm (FPA). The proposed algorithms are applied on several objective functions to identify the FOCS parameters including Mean Square Error (MSE), Integral of Squared Error (ISE), Integral of Absolute Error and Integral of Time Absolute Error. A comparison between the obtained results from each algorithm over each employed objective function is carried out. The target is to investigate the most adequate optimization technique in this difficult multidimensional problem and the best objective function that helps the algorithms capture more accurate and consistent results. The performance of optimization algorithms in the presence of measurement noise has been tested using two objective functions (MSE and ISE) for the three chaotic systems. The overall outcome shows that FPA with ISE objective function is the most efficient combination for the parameter identification of the three FOCS without/with noise because it achieves higher accuracy and more robust results with faster convergence speeds than all other algorithms.


Fractional-order chaotic systems Salp Swarm Algorithm Whale Optimization Algorithm Moth-Flame Optimizer Grey Wolf Optimizer Flower Pollination Algorithm IAE ISE ITAE MSE 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Electrical Engineering, Faculty of EngineeringFayoum UniversityFayoumEgypt
  2. 2.Engineering Mathematics and Physics Department, Faculty of EngineeringFayoum UniversityFayoumEgypt
  3. 3.Nanoelectronics Integrated Systems Center (NISC)Nile UniversityGizaEgypt
  4. 4.Department of Electrical and Computer EngineeringUniversity of SharjahSharjahUnited Arab Emirates
  5. 5.Department of Electrical and Computer EngineeringUniversity of CalgaryCalgaryCanada
  6. 6.Engineering Mathematics and Physics Department, Faculty of EngineeringCairo UniversityGizaEgypt
  7. 7.Nanoelectronics Integrated Systems Center (NISC)Nile UniversityGizaEgypt

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