RESONANCES AND CHAOS IN PARAMETRIC SYSTEMS

Time-periodic systems close to two-dimensional non-linear Hamiltonian systems are studied in the case when the perturbation contains non-linear parametric terms and is non-conservative. A condition for the existence of new regimes in the resonance zones, namely, regular two-frequency and irregular ''quasi-attractors'' is established. The problem of the transition from the resonance case to the nonresonance one as the difference in tuning frequency is altered is solved by analysing self-excited oscillatory truncated systems determining the topology of the resonance zones. Using a specific example, it is shown that the numerical and analytic results are in good agreement in the quasi-conservative case.