Analytical solutions of a generalized Duffing-harmonic oscillator by a nonlinear time transformation method

► A nonlinear transformation is proposed for a generalized Duffing-harmonic oscillator. ► The relative error of period with respect to the exact one is always very small. ► Approximate solution of homoclinic/heteroclinic orbits can be obtained. ► Phase portraits are in excellent agreement even at homoclinic/heteroclinic orbits.