Interplay between solitary states and chimeras in multiplex neural networks

Abstract

We study numerically the spatiotemporal dynamics and synchronization of a heterogeneous two-layer multiplex network where each layer is represented by a ring of nonlocally coupled FitzHugh–Nagumo neurons in the oscillatory regime. Being uncoupled, individual layers can show chimera states, solitary states and combined structures (the coexistence of chimera and solitary states) depending on the values of the intralayer coupling parameters and initial conditions. We choose different spatiotemporal patterns in the coupled layers and systematically study synchronization between them when the interlayer coupling is introduced through either the fast (activator) or the slow (inhibitor) variable of the FitzHugh–Nagumo oscillators. Our results enable to uncover the competitive behavior between the solitary states and the chimeras in the transition to synchronous regime in the considered network. We also analyze the synchronization peculiarities for two different types of the interlayer coupling by using the local and global synchronization measures.