Transition from quasiperiodicity to chaos of a soliton oscillator

We study the properties of the quasiperiodic attractors of the driven and damped sine-Gordon system close to the onset of chaotic dynamics. Our system is a perturbed sine-Gordon equation with ac and dc forcing terms over a finite-sized spatial interval. In this system the quasiperiodic trajectories are generated by the incommensurability of the soliton oscillation and external drive frequencies. For increasing values of the ac drive amplitude the attractors of the system, displayed in a spatially averaged Poincaré section, present the characteristic folding and mixing properties of the transition to chaos through quasiperiodicity. In the parameter plane that we scan, the basic features of the transition are not dependent upon the particular ac drive amplitude and frequency causing the transition. Analysis of the singularity spectrum f(α) of several attractors at the chaotic threshold exhibits general features of the transition.