Anti-phase synchronization of waves in a multiplex network of van der Pol oscillators

We study numerically the spatiotemporal dynamics and anti-phase synchronization of complex structures in a two-layer multiplex network of bidirectionally and repulsively coupled two-dimensional lattices. Each layer consists of locally and attractively coupled identical van der Pol oscillators. Depending on randomly distributed initial conditions the isolated layers can exhibit either a spiral or a target wave regime. The latter is found for first time for the locally coupled van der Pol lattice considered in this work. We vary the inter-layer coupling strength for either fixed or changing intra-layer coupling strengths in the interacting layers. The numerical results are summarized in the two-dimensional diagrams plotted in the "intra-layer coupling strength - inter-layer coupling strength " parameter plane. Anti-phase synchronization is identified by evaluating the local and global cross -correlation coefficients which are equal to-1. We also explore the impact of random de-multiplexing on the robustness of the observed spatiotemporal structures and anti-phase synchronized regimes in the two-layer network.