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)

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.