NUMERICAL SIMULATION OF THE FRACTIONAL-ORDER RÖSSLER CHAOTIC SYSTEMS WITH GRÜNWALD–LETNIKOV FRACTIONAL DERIVATIVE

Xiaoyu Li and Yu-Lan Wang
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Xiaoyu Li: College of Science, Inner Mongolia University of Technology, Hohhot 010051, P. R. China‡College of Date Science and Application, Inner Mongolia University of Technology, Hohhot 010080, P. R. China
Yu-Lan Wang: College of Science, Inner Mongolia University of Technology, Hohhot 010051, P. R. China†Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 08, 1-8

Abstract: In recent years, scholars have studied the chaotic behavior in the fractional dynamic systems and found that the fractional dynamic systems have unique properties that the integer dynamic systems do not have. Therefore, the numerical simulation of fractional chaotic systems is very important. This paper introduces a high-precision numerical method for the fractional-order Rössler chaotic systems. Complex dynamic behavior of the fractional-order Rössler chaotic systems is shown by using the present method. We observe some novel dynamic behaviors in numerical simulation which are unlike any that have been previously found in numerical experiments or theoretical studies. The simulation results of numerical experiments demonstrate the effectiveness of the present method.

Keywords: Fractional Chaotic System; Fractional Rössler System; High-Precision Numerical Method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402290

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