Bifurcations of limit cycles in periodically forced nonlinear systems: the harmonic balance approach

The harmonic balance approach is used to analyze tangent (saddle-node) and flip (period-doubling) bifurcations of limit cycles in periodically forced nonlinear dynamical systems. An algebraic system of equations, whose unknowns are the coefficients of a truncated Fourier series, is defined and the relationships between the bifurcations of the solutions of this algebraic system and the tangent and flip bifurcations of the limit cycles are pointed out. Some examples are presented to illustrate the method and its accuracy