04-123 Michele V. Bartuccelli, Alberto Berretti, Jonathan H.B. Deane, Guido Gentile, Stephen A. Gourley
Periodic orbits and scaling laws for a driven damped quartic oscillator (2401K, pdf) Apr 20, 04
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Abstract. In this paper we investigate the conditions under which periodic solutions of a certain nonlinear oscillator persist when the differential equation is perturbed by adding a driving periodic force and a dissipative term. We conjecture that for any periodic orbit, characterized by its frequency, there exists a threshold for the damping coefficient, above which the orbit disappears, and that this threshold is infinitesimal in the perturbation parameter, with integer order depending on the frequency. Some rigorous analytical results toward the proof of these conjectures are provided. Moreover the relative size and shape of the basins of attraction of the existing stable periodic orbits are investigated numerically, giving further support to the validity of the conjectures.

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