A modified elliptic Lindstedt–Poincaré method for certain strongly non-linear oscillators

A modified elliptic Lindstedt–Poincaré method is presented for the steady state analysis of strongly non-linear oscillators of the form ẍ+c1x+c3x3=εf(x,ẋ), in which a new parameter α=α(ε) is employed such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the above strongly non-linear oscillators with large parameter ε is transformed into a small parameter system with respect to α.