A perturbation-incremental method for the calculation of semi-stable limitcycles of strongly non-linear oscillators

The semi-stable limit cycle and bifurcation of strongly non-linear oscillat ors of the form (x) double over dot + g(x) = lambda f(x, (x) over dot, mu)( x) over dot is studied by the perturbation-incremental method. Firstly, the ordinary differential equation is transformed into an integral equation by a non-linear time transformation, then the initial solution for lambda app roximate to 0 is obtained by using the perturbation method. Secondly, the s olution for an arbitrary value of lambda can be determined by using the inc remental approach. Two examples are given to show the efficiency and accura cy of the present method. Copyright (C) 2000 John Wiley & Sons, Ltd.