On the road towards multidimensional tori
  The problem of persistence of four-frequency tori is considered in models represented by the coupled periodically driven self-oscillators. We show that the adding the third oscillator gives rise to destruction of the three-frequency tori, with appearance of regions of either chaotic attractors or four-frequency tori. As the coupling strength decreases, the four-frequency tori dominate, and the amplitude threshold of their occurrence vanishes. Also, for three oscillators, a domain of complete synchronization of the system by the external driving can disappear. 
A.P. Kuznetsov, I.R. Sataev, L.V. Turukina
nlin.CD