Wave patterns in two-dimensional networks of non-locally coupled oscillators with phase delay

Abstract

We studied the wave patterns in non-locally, repulsively coupled oscillators on a 2D lattice. The repulsive coupling is tuned by the phase delay $\alpha \pi$ and the wave patterns are found in the regime $\alpha \in \left[0.5, 1\right]$. We focused on the growth of orientationally correlated domains and found that the average total boundary size $\overline{|B|}$ obeys an approximate power law $\overline{|B|}\propto t^{-b}$ for $\alpha = 0.8$ and $\alpha =0.9$. In contrast, at $\alpha = 0.7$, the dynamics is disrupted by defect-mediated domain formation and domain splitting. The fitting-window dependence of the apparent exponent $b$, as well as the mean and standard deviation of the wave speed $c$, decreases with increasing $\alpha$, which is consistent with the linear stability analysis of the wave solution.