ON THE STRUCTURE OF RESONANCE ZONES AND CHAOS IN NONLINEAR PARAMETRIC SYSTEMS

Abstract

Periodic-in-time systems close to two-dimensional nonlinear Hamiltonian ones are analyzed in the case when a perturbation contains nonlinear parametric terms and it is nonconservative. The existence of new regimes in the resonance zone, regular two-frequency regimes and non-regular “quasi-attractors,” is determined. The problem of transition from a resonance case to a nonresonance one for a changing detuning is solved on the basis of the analysis of shortened auto-oscillatory systems that determine the topology of the resonance zones. The theoretical results of this investigation are illustrated on a computer for a specific example. In the quasi-conservative case the numerical and analytical results are in good agreement.