Open Access

ARTICLE

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

Dandan Dai¹, Xiaoyu Li², Zhiyuan Li², Wei Zhang³, Yulan Wang^2,*
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. https://doi.org/10.32604/cmes.2022.022323

Received 04 March 2022; Accepted 09 June 2022; Issue published 27 October 2022

Abstract

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.

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Keywords

Novel complex dynamic behavior; numerical simulation; fractional-order lorenz chaotic systems; high-precision

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