A hyperbolic perturbation method for determining homoclinic solution of certain strongly nonlinear autonomous oscillators

A hyperbolic perturbation method is presented for determining the homoclinic solution of certain strongly nonlinear autonomous oscillators of the form x ¨ + c 1 x + c 2 x 2 = ε f ( μ , x , x ˙ ) in which hyperbolic functions can be employed instead of the usual periodic functions in the perturbation procedure. The generalized van der Pol oscillator in which f ( μ , x , x ˙ ) = ( μ + μ 1 x - μ 2 x 2 ) x ˙ is studied. To illustrate the accuracy of the present method, its predictions are compared with those of Runge-Kutta method.