Repulsive inter-layer coupling induces anti-phase synchronization

We present numerical results for the synchronization phenomena in a bilayer network of repulsively coupled 2D lattices of van der Pol oscillators. We consider the cases when the network layers have either different or the same types of intra-layer coupling topology. When the layers are uncoupled, the lattice of van der Pol oscillators with a repulsive interaction typically demonstrates a labyrinth-like pattern, while the lattice with attractively coupled van der Pol oscillators shows a regular spiral wave structure. We reveal for the first time that repulsive inter-layer coupling leads to anti-phase synchronization of spatiotemporal structures for all considered combinations of intra-layer coupling. As a synchronization measure, we use the correlation coefficient between the symmetrical pairs of network nodes, which is always close to -1 in the case of anti-phase synchronization. We also study how the form of synchronous structures depends on the intra-layer coupling strengths when the repulsive inter-layer coupling is varied. Published under an exclusive license by AIP Publishing.

Automated summary

In a bilayer network of van der Pol oscillators with repulsive coupling, anti-phase synchronization of spatiotemporal structures was observed for all considered combinations of intra-layer coupling. The correlation coefficient between symmetrical pairs of network nodes tended to be close to -1 in the case of anti-phase synchronization. The form of synchronous structures depended on the intra-layer coupling strengths, which varied with the repulsive inter-layer coupling.