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The Multistage Homotopy Perturbation Method for Solving Chaotic and Hyperchaotic Lü System

Author

Listed:
  • M. S. H. Chowdhury
  • Nur Isnida Razali
  • Waqar Asrar
  • M. M. Rahman

Abstract

The multistage homotopy‐perturbation method (MHPM) is applied to the nonlinear chaotic and hyperchaotic Lü systems. MHPM is a technique adapted from the standard homotopy‐perturbation method (HPM) where the HPM is treated as an algorithm in a sequence of time intervals. To ensure the precision of the technique applied in this work, the results are compared with a fourth‐order Runge‐Kutta method and the standard HPM. The results show that the MHPM is an efficient and powerful technique in solving both chaotic and hyperchaotic systems.

Suggested Citation

  • M. S. H. Chowdhury & Nur Isnida Razali & Waqar Asrar & M. M. Rahman, 2015. "The Multistage Homotopy Perturbation Method for Solving Chaotic and Hyperchaotic Lü System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:398027
    DOI: 10.1155/2015/398027
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    References listed on IDEAS

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    1. Chen, Aimin & Lu, Junan & Lü, Jinhu & Yu, Simin, 2006. "Generating hyperchaotic Lü attractor via state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 103-110.
    2. Goh, S.M. & Noorani, M.S.M. & Hashim, I., 2009. "Efficacy of variational iteration method for chaotic Genesio system – Classical and multistage approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2152-2159.
    3. Hashim, I. & Chowdhury, M.S.H. & Mawa, S., 2008. "On multistage homotopy-perturbation method applied to nonlinear biochemical reaction model," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 823-827.
    4. Hossein Jafari & Khadijeh Bagherian & Seithuti P. Moshokoa, 2014. "Homotopy Perturbation Method to Obtain Positive Solutions of Nonlinear Boundary Value Problems of Fractional Order," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Chowdhury, M.S.H. & Hashim, I. & Momani, S., 2009. "The multistage homotopy-perturbation method: A powerful scheme for handling the Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1929-1937.
    6. Hossein Jafari & Khadijeh Bagherian & Seithuti P. Moshokoa, 2014. "Homotopy Perturbation Method to Obtain Positive Solutions of Nonlinear Boundary Value Problems of Fractional Order," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, June.
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