Twisted states in low-dimensional hypercubic lattices

Twisted states with non-zero winding numbers have been observed in a ring composed of sinusoidally coupled identical oscillators. In this presentation, we consider finite-sized d-dimensional hypercubic lattices, namely square (d=2) and cubic (d=3) lattices with periodic boundary conditions. For identical oscillators, we observe new states where the oscillators belonging to each line (plane) for d=2 (d=3) are phase synchronized with non-zero winding numbers along the perpendicular direction. We note that these states can be reduced into twisted states in a ring with the same winding number if we regard each subset of phase-synchronized oscillators as one single oscillator. For nonidentical oscillators, we observe similar patterns with slightly heterogeneous phases in each line (d=2) and plane (d=3) for random configurations.