Attractiveness of periodic orbits in parametrically forced systemswith time-increasing friction

TL;DR

This study investigates how a time-increasing friction influences the dynamics of a driven cubic oscillator, revealing that gradually increasing damping enlarges the basins of attraction of key resonances, with implications for spin-orbit models.

Contribution

It introduces a numerical analysis of how time-varying friction affects attractor basins in a driven cubic oscillator, highlighting the impact of damping growth rate and final value.

Findings

Basins of attraction of leading resonances are larger with increasing damping.

The scenario depends on the final damping value and growth rate.

Results have implications for the spin-orbit model.

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.