The variational approach to the theory of subharmonic bifurcations (Q1088218)

A multi-time average variational principle is developed for a study of subharmonic bifurcations in a nonlinear ordinary differential equation, and an analytic method is established to calculate the values of the control parameter at the bifurcation points. A specific application is given to the analysis of the Duffing equation ẍ\(+2\lambda \dot x+x- 4x^ 3=f \cos \omega t\). The connection between period-doubling bifurcations and parametric resonance is clarified. With f the control parameter, the critical values are evaluated analytically at a few bifurcation points with the results in excellent agreement with those of the numerical integration.