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

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48 Citations (Scopus)

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. The validity of the method is verified by comparing the approximation series solution with the results obtained using the standard numerical techniques such as Runge-Kutta method.

Original languageEnglish
Pages (from-to)1744-1752
Number of pages9
JournalChaos, Solitons and Fractals
Volume39
Issue number4
DOIs
Publication statusPublished - Feb 28 2009

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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