DYNAMICS OF FRACTIONAL-ORDER LORENZ
SYSTEM APPLYING DIFFERENT NUMERICAL METHODS
Ylldrita Salihi1, Krutan Rasimi2
1Department of Mathematics, University of Tetova
Str.101, Sllatino, Tetovo-1201, NORTH MACEDONIA
2 Department of Mathematics, University of Tetova
Str. of Luboten 96, Tetovo-1201, NORTH MACEDONIA

Abstract

In this paper we numerically study the chaotic behaviors of the fractional-order Lorenz system, considered as a highly simplified model for the wether, comparing Euler's method, Fourth Order Runge-Kutta method (RK4) and Vectorial Fourth Order Runge-Kutta method with an semi-numerical method named as Fractional Multi-step Differential Transformation method (FMDTM), that exploits the power series representation of the solution. The system is shown to display interesting chaotic behavior depending on the third parameter $c=13.93$ (homoclinic orbit) and $c=24.74$ (formed strange attractor) for same initial conditions and fractional order $\alpha=0.998$, which are analyzed by comparing system phase portraits with each other and $\alpha=1$. The fractional derivatives are described in the Caputo sense. The results demonstrate reliability and efficiency of the algorithm developed using Mathematica Package.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 2
Year: 2022

DOI: 10.12732/ijam.v35i2.8

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