FM 06-2012 (arXiv:1207.4319; mp_arc 12-77)

Author: Michele Bartuccelli, Jonathan Deane and Guido Gentile

Title: Attractiveness of periodic orbits in parametrically forced systems with time-increasing friction
 
Abstract: We consider dissipative one-dimensional systems subject to a periodic force and study numerically how a time-varying friction affects the dynamics. As a model system, particularly suited for numerical analysis, we investigate the driven cubic oscillator in the presence of friction. We find that, if the damping coefficient increases in time up to a final constant value, then the basins of attraction of the leading resonances are larger than they would have been if the coefficient had been fixed at that value since the beginning. From a quantitative point of view, the scenario depends both on the final value and the growth rate of the damping coefficient. The relevance of the results for the spin-orbit model are discussed in some detail.

Keywords: Dissipative systems; Time-dependent friction; Periodic motions; Periodically forced systems; Periodic attractors; Basins of attraction; Bifurcations; Melnikov problem.

Michele V. Bartuccelli
Department of Mathematics
Surrey University
Guildford, GU2 7HX, UK
e-mail: m.bartuccelli@surrey.ac.uk

Jonathan H.B. Deane
Department of Mathematics
Surrey University
Guildford, GU2 7HX, UK
e-mail: j.deane@surrey.ac.uk

Guido Gentile
Dipartimento di Matematica
Università di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@mat.uniroma3.it