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Modelling and numerical synchronization of chaotic system with fractional-order operator

  • Kolade M. Owolabi ORCID logo EMAIL logo
Published/Copyright: November 29, 2021
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 23 Issue 7-8

Abstract

Numerical solution of nonlinear chaotic fractional in space reaction–diffusion system is considered in this paper on a large but finite spatial domain size x ∈ [0, L] for L ≫ 0, x = x(x, y) and t ∈ [0, T]. The classical order chaotic ordinary differential equation is formulated by introducing the second-order spatial fractional derivative with order β ∈ (1, 2]. This second order spatial derivative is modelled by using the definition of the Riesz fractional derivative. The method of approximation combines the Fourier spectral method with the novel exponential time difference schemes. The proposed technique is known to have gained spectral accuracy over finite difference schemes. Applicability and suitability of the suggested methods are tested on Rössler chaotic system of recurring interests in one and two dimensions.

Keywords: chaotic systems; exponential time-differencing methods; fractional reaction–diffusion; numerical simulations; spectral algorithms
2010 Mathematics Subject Classification: 26A33; 35K57; 65L05; 65M06; 93C10
Corresponding author: Kolade M. Owolabi, Department of Mathematical Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria; and Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa, E-mail:

  1. Author contributions: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The author has no conflict of interest regarding this article.

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Received: 2020-06-03
Revised: 2021-06-10
Accepted: 2021-11-04
Published Online: 2021-11-29
Published in Print: 2022-12-16

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2020-0128
Keywords for this article
chaotic systems; exponential time-differencing methods; fractional reaction–diffusion; numerical simulations; spectral algorithms

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  2. Original Research Articles
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  8. Power minimization of gas transmission network in fully transient state using metaheuristic methods
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  10. Higher order rogue waves for the(3 + 1)-dimensional Jimbo–Miwa equation
  11. Dynamic characteristics of supersonic turbulent free jets from four types of circular nozzles
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  13. Chaos and bifurcations in a discretized fractional model of quasi-periodic plasma perturbations
  14. Wavelet collocation methods for solving neutral delay differential equations
  15. Numerical solution of highly non-linear fractional order reaction advection diffusion equation using the cubic B-spline collocation method
  16. Solving nonlinear third-order boundary value problems based-on boundary shape functions
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