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

Fathi M. Allan

Chaos, Solitons & Fractals, 2009, vol. 39, issue 4, 1744-1752

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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:39:y:2009:i:4:p:1744-1752

DOI: 10.1016/j.chaos.2007.06.116

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