Perturbation-iterative method for determining limit cycles of strongly non-linear oscillators

A perturbation-iterative method is presented for determining limit cycles of strongly non-linear oscillators of the form x^.. + g(x) =Q μf(x,x^.), where g(x) is an arbitrary non-linear function of the displacement x, and μ has a small to moderate value. By assuming that x = a cos φ + b and dφ /dt = Φ (φ), where Φ (φ) is 2π-periodic in φ, the method allows a, b and Φ (φ) to be calculated to any desired degree of accuracy by the iterative method, and the limit cycle phase portraits are in very good agreement with the corresponding numerical solutions of the differential equations.