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 Poincaré 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.

我们报告了一个小的次谐波扰动被添加到驱动松弛振荡器的2D圆环特征时获得的3D圆环的不稳定的实验证据。庞加莱部分表明，圆环破裂对主驱动频率与其第一副谐波扰动分量之间的相位差很敏感。观察到的过渡确定了Newhouse，Ruelle和Takens拟周期性过渡到3D圆环上的混沌。正弦摄动的圆图上的数值结果反映了实验结果，并证实了相差在不同动力状态之间过渡中的关键作用。