An efficient method for switching branches of period-doubling bifurcations of strongly non-linear autonomous oscillators with many degrees of freedom

Popular algorithms for switching branches at a bifurcation point of strongly non-linear oscillators are generally quite involved as they require the computation of the tangent of a new branch and second derivatives. In this paper, a simple but efficient algorithm is presented by using a perturbation-incremental method for switching branches at a period-doubling bifurcation of strongly non-linear autonomous oscillators with many degrees of freedom. To switch to a new branch at a bifurcation point, a parameter is simply turned on from zero to a small positive value so as to obtain an initial solution on the emanating branch for subsequent continuation. The parametric value at a period-doubling bifurcation can also be determined accurately. Furthermore, limit cycles of period 2k (k⩾1) can be calculated to any desired degree of accuracy.