On a Peculiar Attractor for Weakly Nonlinear Oscillators with a Two Period Quasiperiodic Forcing

Abstract

We study a very peculiar nonlinear oscillator with an external two period quasiperiodic excitation, being the golden mean the ratio between the two frequencies. The two period quasi periodic forcing is characterized by an infinite frequencies number. As a consequence, we find that the motion settles down in a two period quasi periodic atttractor for a wide excitation amplitude range. The competition between the two frequencies does not produce a closed curve but fills a well defined phase space region in the Poincarè section. This attractor somehow resembles strange nonchaotic attractors because both are characterized by quasiperiodic forcing. Using a suitable perturbation method, we can understand the new attractor most important characteristics and find an approximate solution for its dynamical behavior. Numerical simulations are used to check out the analytical investigation.