Аннотация:
We consider nonconservative quasi-periodic perturbations of two-dimensional Hamiltonian
systems with nonmonotonic rotation. The peculiarity of these systems is that degenerate resonances can take place. Special focus is on those systems for which the corresponding autonomous
perturbed system has a structurally stable limit cycle. If the cycle appears in the neighborhood
of a nonresonance phase curve, then it corresponds to an invariant torus in the initial system.
In this regard, the problem of synchronization arises when the invariant torus passes through
a resonance zone. In this paper, we distinguish a class of perturbations (the so-called parametric
perturbations) under which synchronization can be violated. Also, we introduce the concept of
generalized synchronization and give conditions for this type of synchronization to occur. As an
example, we study a Duffing-like equation with an asymmetric potential function.
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