Resonant parametric perturbations of the Hopf bifurcation

AbstractThe effects of periodic parametric perturbations on a system undergoing Hopf bifurcation are studied in detail. Of primary interest is the case of resonance between the Hopf bifurcation frequency and the perturbation frequency. Method of alternative problems is used to obtain the small nonlinear periodic solutions. It is shown that for a certain range of parameters, the Hopf solution is modified to give rise to jump response as well as isolated solutions. For some parameter combinations, stable solutions can get unstable and may bifurcate into aperiodic or amplitude modulated motions