ON THE ONSET OF CHAOTIC DYNAMICS IN ASYMMETRIC OSCILLATORS

The onset of chaotic dynamics in a driven and damped nonlinear oscillator is studied using the Melnikov method. We have turned special attention to the influence of an asymmetry parameter in the equation of motion. In contrast to the symmetric case the bifurcation function has singularities on a discrete set of frequencies. The method of harmonic balance qualitatively supports some of the results of the Melnikov method. For selected parameter values the analytical predictions are checked by numerical calculations.