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Solving Hyperchaotic Systems Using the Spectral Relaxation Method

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  • S. S. Motsa
  • P. G. Dlamini
  • M. Khumalo

Abstract

A new multistage numerical method based on blending a Gauss-Siedel relaxation method and Chebyshev pseudospectral method, for solving complex dynamical systems exhibiting hyperchaotic behavior, is presented. The proposed method, called the multistage spectral relaxation method (MSRM), is applied for the numerical solution of three hyperchaotic systems, namely, the Chua, Chen, and Rabinovich-Fabrikant systems. To demonstrate the performance of the method, results are presented in tables and diagrams and compared to results obtained using a Runge-Kutta-(4,5)-based MATLAB solver, ode45 , and other previously published results.

Suggested Citation

  • S. S. Motsa & P. G. Dlamini & M. Khumalo, 2012. "Solving Hyperchaotic Systems Using the Spectral Relaxation Method," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-18, December.
    • Handle: RePEc:hin:jnlaaa:203461
    DOI: 10.1155/2012/203461
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    Cited by:

    1. Vusi Mpendulo Magagula, 2019. "On the Multidomain Bivariate Spectral Local Linearisation Method for Solving Systems of Nonsimilar Boundary Layer Partial Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-18, June.

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