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Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with Caputo Fractional Derivative

Dandan Dai1, Xiaoyu Li2, Zhiyuan Li2, Wei Zhang3, Yulan Wang2,*

1 School of Physics and Electronic Information Engineering, Jining Normal University, Jining, 012000, China
2 Department of Mathematics, Inner Mongolia University of Technology, Hohhot, 010051, China
3 Institute of Economics and Management, Jining Normal University, Jining, 012000, China

* Corresponding Author: Yulan Wang. Email:

(This article belongs to this Special Issue: Fractal-Fractional Models for Engineering & Sciences)

Computer Modeling in Engineering & Sciences 2023, 135(2), 1371-1392.


Although some numerical methods of the fractional-order chaotic systems have been announced, high-precision numerical methods have always been the direction that researchers strive to pursue. Based on this problem, this paper introduces a high-precision numerical approach. Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method. We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies. We investigate the influence of , , on the numerical solution of fractional-order Lorenz chaotic systems. The simulation results of integer order are in good agreement with those of other methods. The simulation results of numerical experiments demonstrate the effectiveness of the present method.


Cite This Article

Dai, D., Li, X., Li, Z., Zhang, W., Wang, Y. (2023). Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with Caputo Fractional Derivative. CMES-Computer Modeling in Engineering & Sciences, 135(2), 1371–1392.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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