BIFURCATION-ANALYSIS VIA HARMONIC-BALANCE IN PERIODIC-SYSTEMS WITH FEEDBACK STRUCTURE

The harmonic balance approach is applied to a class of periodic dynami cal systems with a specific (but quite general) feedback structure, in order to analyse approximately tangent (saddle-node) and flip (period -doubling) bifurcations of periodic solutions. By exploiting the syste m structure, an algebraic system of equations, whose unknowns are the coefficients of a truncated Fourier series, is defined and the relatio nship between the bifurcations of the roots of this algebraic system a nd the tangent and flip bifurcations of the periodic solutions is poin ted out. An example concerning an adaptive control system illustrates the proposed methodology.