Efficient determination of higher-order periodic solutions using n-mode harmonic balance

This paper presents a systematic procedure to explicitly determinethe algebraic equations arising from the method of harmonicbalance with an arbitrary number of modes in the assumed solutions.The technique can be used for a wide variety of nonlinear oscillators(including systems of ordinary differential equations). Themethod is illustrated in the case of second-order differentialequations with nonlinear restoring force. Although numericalmethods have been employed to solve the resulting systems ofalgebraic equations, the general approach is analytic. As such,this study confirms independently (i.e. nonsimulation) the period-doublingcascade of an escape equation including the bifurcation universalscaling laws.