On the destabilization of a periodically driven three-dimensional torus

We report experimental evidence of the destabilization of a 3D torus obtained when a small subharmonic perturbation is added to a 2D torus characteristic of a driven relaxation oscillator. The Poincare sections indicate that the torus breakup is sensitive to the phase difference between the main driving frequency and its first subharmonic perturbing component. The observed transition confirms the Newhouse, Ruelle and Takens quasiperiodic transition to chaos on a 3D torus. Numerical results on a sinusoidally perturbed circle map mirror the experimental results and confirm the key role of the phase difference in the transition between distinct dynamical regimes.

Automated summary

Experimental and numerical results demonstrate that destabilization and breakup of a 3D torus can occur when a small subharmonic perturbation is added to a 2D torus characteristic of a driven relaxation oscillator. The phase difference between the main driving frequency and its first subharmonic perturbing component plays a key role in this transition, confirming the Newhouse, Ruelle, and Takens quasiperiodic transition to chaos.