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Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method

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  • Allan, Fathi M.

Abstract

Based on a new kind of analytic method, namely the Homotopy analysis method, an analytic approach to solve non-linear, chaotic system of ordinary differential equations is presented. The method is applied to Lorenz system; this system depends on the three parameters: σ, b and the so-called bifurcation parameter R are real constants. Two cases are considered. The first case is when R=20.5 which corresponds to the transition region and the second case corresponds to R=23.5 which corresponds to the chaotic region.

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  • Allan, Fathi M., 2009. "Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1744-1752.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1744-1752
    DOI: 10.1016/j.chaos.2007.06.116
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    References listed on IDEAS

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    1. Wu, Yongyan & Wang, Chun & Liao, Shi-Jun, 2005. "Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1733-1740.
    2. Wu, Wan & Liao, Shi-Jun, 2005. "Solving solitary waves with discontinuity by means of the homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 177-185.
    3. He, Ji-Huan, 2007. "Variational approach for nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1430-1439.
    4. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    5. Tan, Yue & Xu, Hang & Liao, Shi-Jun, 2007. "Explicit series solution of travelling waves with a front of Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 462-472.
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