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Simple estimation method for the largest Lyapunov exponent of continuous fractional-order differential equations

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  • Zhou, Shuang
  • Wang, Xingyuan

Abstract

In this paper, a simple method based on the perturbation of the initial value is presented to directly estimate the largest Lyapunov exponent (LLE) from continuous fractional-order differential equations. Two nearby trajectories are used to directly compute the LLE and reduce parameter errors. Another initial value is obtained by perturbing the given initial value. Two solutions are then developed from a fractional-order chaotic system by using the two initial values. The evolutionary distance between the two solutions is calculated, and the LLE is determined from the curve of the track distance. Some continuous fractional-order chaotic and nonchaotic differential equations are applied to verify the effectiveness of our method. Experimental results indicate that the proposed method is feasible and easy to implement instead of computing the Jacobian matrix and phase space.

Suggested Citation

  • Zhou, Shuang & Wang, Xingyuan, 2021. "Simple estimation method for the largest Lyapunov exponent of continuous fractional-order differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    • Handle: RePEc:eee:phsmap:v:563:y:2021:i:c:s0378437120307834
    DOI: 10.1016/j.physa.2020.125478
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    References listed on IDEAS

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    Cited by:

    1. Jose-Cruz Nuñez-Perez & Vincent-Ademola Adeyemi & Yuma Sandoval-Ibarra & Francisco-Javier Perez-Pinal & Esteban Tlelo-Cuautle, 2021. "Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    2. Wang, Jieyang & Mou, Jun & Xiong, Li & Zhang, Yingqian & Cao, Yinghong, 2021. "Fractional-order design of a novel non-autonomous laser chaotic system with compound nonlinearity and its circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Li, Hang & Shen, Yongjun & Han, Yanjun & Dong, Jinlu & Li, Jian, 2023. "Determining Lyapunov exponents of fractional-order systems: A general method based on memory principle," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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