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

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.