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¨+c1x+c2x2=εf(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+μ1x-μ2x2)x˙ is studied. To illustrate the accuracy of the present method, its predictions are compared with those of Runge-Kutta method.