  We explore numerically the synchronization effects in a heterogeneous
two-layer network of two-dimensional (2D) lattices of van der Pol
oscillators.The inter-layer coupling of the multiplex network has an attractive
character. One layer of 2D lattices is characterized by attractive coupling of
oscillators and demonstrates a spiral wave regime for both the local and
nonlocal interaction. The oscillators in the second layer are coupled through
active elements and the interaction between them has the repulsive character.
We show that the lattice with the repulsive type of coupling demonstrates
complex spatiotemporal cluster structures, which can be called as
labyrinth-like structures. We show for the first time that this multiplex
network with fundamentally different types of intra-layer coupling demonstrates
the mutual synchronization and a competition between two types of structures.
Our numerical study indicates that the synchronization threshold and the type
of spatiotemporal patterns in both the layers strongly depend on the ratio of
the intra-layer coupling strength of the two lattices. We also analyze the
impact of intra-layer coupling ranges on the synchronization effects.
