Solving Hyperchaotic Systems Using the Spectral Relaxation Method
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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/203461 |
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| author | S. S. Motsa P. G. Dlamini M. Khumalo |
| author_facet | S. S. Motsa P. G. Dlamini M. Khumalo |
| author_sort | S. S. Motsa |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d1905bc21c5e431cb24b7f7ea8d9f1e3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d1905bc21c5e431cb24b7f7ea8d9f1e32025-02-03T01:23:39ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/203461203461Solving Hyperchaotic Systems Using the Spectral Relaxation MethodS. S. Motsa0P. G. Dlamini1M. Khumalo2School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg, Scottsville 3209, South AfricaDepartment of Mathematics, University of Johannesburg, P.O. Box 17011, Doornfontein 2028, South AfricaDepartment of Mathematics, University of Johannesburg, P.O. Box 17011, Doornfontein 2028, South AfricaA 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.http://dx.doi.org/10.1155/2012/203461 |
| spellingShingle | S. S. Motsa P. G. Dlamini M. Khumalo Solving Hyperchaotic Systems Using the Spectral Relaxation Method Abstract and Applied Analysis |
| title | Solving Hyperchaotic Systems Using the Spectral Relaxation Method |
| title_full | Solving Hyperchaotic Systems Using the Spectral Relaxation Method |
| title_fullStr | Solving Hyperchaotic Systems Using the Spectral Relaxation Method |
| title_full_unstemmed | Solving Hyperchaotic Systems Using the Spectral Relaxation Method |
| title_short | Solving Hyperchaotic Systems Using the Spectral Relaxation Method |
| title_sort | solving hyperchaotic systems using the spectral relaxation method |
| url | http://dx.doi.org/10.1155/2012/203461 |
| work_keys_str_mv | AT ssmotsa solvinghyperchaoticsystemsusingthespectralrelaxationmethod AT pgdlamini solvinghyperchaoticsystemsusingthespectralrelaxationmethod AT mkhumalo solvinghyperchaoticsystemsusingthespectralrelaxationmethod |