Numerical solutions and synchronization of a variable-order fractional chaotic system

Zakia Hammouch; Mehmet Yavuz; Necati Özdemir

doi:10.53391/mmnsa.2021.01.002

EN

Numerical solutions and synchronization of a variable-order fractional chaotic system

Abstract

In the present paper, we implement a novel numerical method for solving differential equations with fractional variable-order in the Caputo sense to research the dynamics of a circulant Halvorsen system. Control laws are derived analytically to make synchronization of two identical commensurate Halvorsen systems with fractional variable-order time derivatives. The chaotic dynamics of the Halvorsen system with variable-order fractional derivatives are investigated and the identical synchronization between two systems is achieved. Moreover, graph simulations are provided to validate the theoretical analysis.

Keywords

Variable-order fractional derivative, chaotic system, Lyapunov exponent, synchronization

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Details

Primary Language

English

Subjects

Applied Mathematics

Journal Section

Research Article

Authors

Zakia Hammouch This is me
0000-0001-7349-6922
Morocco

Mehmet Yavuz
0000-0002-3966-6518
Türkiye

Necati Özdemir ^* This is me
0000-0002-6339-1868
Türkiye

Publication Date

September 30, 2021

Submission Date

July 13, 2021

Acceptance Date

August 17, 2021

Published in Issue

Year 2021 Volume: 1 Number: 1

DOI

https://doi.org/10.53391/mmnsa.2021.01.002

IZ

https://izlik.org/JA72ZF47ZT

APA

Hammouch, Z., Yavuz, M., & Özdemir, N. (2021). Numerical solutions and synchronization of a variable-order fractional chaotic system. Mathematical Modelling and Numerical Simulation With Applications, 1(1), 11-23. https://doi.org/10.53391/mmnsa.2021.01.002

AMA

1.Hammouch Z, Yavuz M, Özdemir N. Numerical solutions and synchronization of a variable-order fractional chaotic system. MMNSA. 2021;1(1):11-23. doi:10.53391/mmnsa.2021.01.002

Chicago

Hammouch, Zakia, Mehmet Yavuz, and Necati Özdemir. 2021. “Numerical Solutions and Synchronization of a Variable-Order Fractional Chaotic System”. Mathematical Modelling and Numerical Simulation With Applications 1 (1): 11-23. https://doi.org/10.53391/mmnsa.2021.01.002.

EndNote

Hammouch Z, Yavuz M, Özdemir N (September 1, 2021) Numerical solutions and synchronization of a variable-order fractional chaotic system. Mathematical Modelling and Numerical Simulation with Applications 1 1 11–23.

IEEE

[1]Z. Hammouch, M. Yavuz, and N. Özdemir, “Numerical solutions and synchronization of a variable-order fractional chaotic system”, MMNSA, vol. 1, no. 1, pp. 11–23, Sept. 2021, doi: 10.53391/mmnsa.2021.01.002.

ISNAD

Hammouch, Zakia - Yavuz, Mehmet - Özdemir, Necati. “Numerical Solutions and Synchronization of a Variable-Order Fractional Chaotic System”. Mathematical Modelling and Numerical Simulation with Applications 1/1 (September 1, 2021): 11-23. https://doi.org/10.53391/mmnsa.2021.01.002.

JAMA

1.Hammouch Z, Yavuz M, Özdemir N. Numerical solutions and synchronization of a variable-order fractional chaotic system. MMNSA. 2021;1:11–23.

MLA

Hammouch, Zakia, et al. “Numerical Solutions and Synchronization of a Variable-Order Fractional Chaotic System”. Mathematical Modelling and Numerical Simulation With Applications, vol. 1, no. 1, Sept. 2021, pp. 11-23, doi:10.53391/mmnsa.2021.01.002.

Vancouver

1.Zakia Hammouch, Mehmet Yavuz, Necati Özdemir. Numerical solutions and synchronization of a variable-order fractional chaotic system. MMNSA. 2021 Sep. 1;1(1):11-23. doi:10.53391/mmnsa.2021.01.002