Transition of Chimera States and Synchronization in Two-Layer Networks of Coupled Hindmarsh–Rose Neurons

The present work focuses on the existence of chimera states in two-layer networks of locally, nonlocally, and globally coupled Hindmarsh–Rose neurons. We show that chimera states occur in all three coupled neuronal networks by changing synaptic coupling strength and the number of coupled neighbors, and traveling chimera state exists in networks by using local and nonlocal couplings. Particularly, we find that in the nonlocally coupled network, there exist regions of coherent state, which can produce a wave such that the period becomes longer with the increase of the number of coupled neighbors. Interestingly, we observe a new chimera state with the coexistence of interlayer synchronous and asynchronous chimera states, which we named as the interlayer semi-synchronous chimera state. In addition, the results indicate that the interaction between layers in neuronal networks can induce different types of chimera states and firing patterns, which could be useful to control neural firing patterns and deepen the understanding of neuronal evolution where coherent and incoherent dynamics coexist.