Attractiveness of periodic orbits in parametrically forced systemswith 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.

30 pages, 6 figures

References in corpus (2)

• Mercury's capture into the 3/2 spin-orbit resonance including the effect of core-mantle friction
• Emerging attractors and the transition from dissipative to conservative dynamics

Cited by in corpus (5)

• The high-order Euler method and the spin-orbit model A fast algorithm for solving differential equations with small, smooth nonlinearity
• Periodic and quasi-periodic attractors for the spin-orbit evolution of Mercury with a realistic tidal torque
• Basins of attraction in forced systems with time-varying dissipation
• The effects of time-dependent dissipation on the basins of attraction for the pendulum with oscillating support
• Pseudo-synchronous solutions for dissipative non-autonomous systems