Globally and locally attractive solutions for quasi-periodically forced systems

We consider a class of differential equations, x + yx + g(x) = f(omega t), with omega is an element of R-d, describing one-dimensional dissipative systems subject to a periodic or quasi-periodic (Diophantine) forcing. We study existence and properties of trajectories with the same quasi-periodicity as the forcing. For g(x) = x(2p+1), p is an element of N, we show that, when the dissipation coefficient is large enough, there is only one such trajectory and that it describes a global attractor. In the case of more general nonlinearities, including g(x) = x(2) (describing the varactor equation), we find that there is at least one trajectory which describes a local attractor.