Behavior of Phase-Inversion Waves on Coupled Van der Pol Oscillators as a Torus

We have been investigating various synchronization phenomena which are observed on some kinds of shape of coupled oscillator networks. Especially, we have been investigating and analyzing phase-inversion waves which continuously propagate with inverting phase states between adjacent oscillators on a ladder, a ring, and 2D-lattice of coupled oscillators. In this paper, we investigate what kinds of behavior of the phase-inversion waves on coupled van der Pol oscillators as a torus.