External Synchronization of Solitary States and Chimeras in Unidirectionally Coupled Neural Networks

We perform numerical simulation of the dynamics of a multiplex network consisting of two unidirectionally coupled rings of FitzHugh-Nagumo neurons with nonlocal interaction. When uncoupled, one ring demonstrates solitary state regimes and the other one exhibits chimera states. We explore in detail how the synchronization degree between the layers depends on the type of unidirectional interlayer coupling (via fast or slow variables) and on the structures in the driver layer. It is shown that the structure in the response layer can be suppressed and is replaced by the driver layer structure. However, the degree of external synchronization is higher in the case when the driver layer demonstrates solitary states and when the unidirectional coupling is executed via the fast variables. In the case of coupling via the slow variables, external synchronization of neither solitary states nor chimeras cannot be achieved in the considered network.