Abstract
In this paper we investigate the impact of competition between layers of adaptive multiplex network on pattern formation in the system under study and discuss the possibility of the further application of the obtained results for the analysis of the neural network of brain. To describe the dynamics of interacting nodes we use the Kuramoto model of coupled phase oscillators. To understand the macroscopic processes that take place in this system we calculate and compare the values of layer and global order parameter, which describe the degree of coherence between the nodes in each layer and over whole network, respectively. We find that in such adaptive network the low values of order inside layers corresponding to the formation of similar topologies among them. Nevertheless, the cluster synchronization results in divergence of layer structures from each other.
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