Synchronization in two-layer networks of chaotic oscillators via a double distributed control

In some of the real-world networks, the interacting agents synchronize in groups or clusters, not in a complete way; and also, many networks can be modeled by multi-layer networks where nodes are coupled in several independent networks. In this work, we deal with the problem of synchronizing a pair of layers of networks via a double distributed control. Specifically, these controllers depends on the degree of nodes. Our first aim is synchronizing just some nodes of each layer, and then as a second goal, we apply a control to the already synchronized nodes of each layer to assure that they follow the same dynamics in both layers.