Coherent and incoherent control in neuronal networks based on two sub-networks and biological implication

Chimera states are fascinating phenomena nowadays and are largely discussed in neuroscience in the aim to describe the coexistence between coherent and incoherent states observed in complex neuronal networks. The case of brain is a typical example, where depending on the problem observed for instance neurodegenerative diseases, some regions on the cerebral cortex can show coherent or incoherent dynamics. Coherent dynamics is associated to the synchronization of different nodes of network constituted while incoherent dynamics are linked to the desynchronization. In this work, we analyze the emergence of chimera states in a network designed by two sub-networks interacting with electrical and chemical synapses. We observe that with the help of a controller on a group of nodes, it is possible to significantly achieve coherence or incoherence of cluster oscillators in a network. The control strategy consists to consider both sub-networks with different types of inter-layer connections (electrical and chemical) between links. In addition, a possibility to find a global synchronization in the network and an issue to explain the behavior of brain in case of some neurodegenerative diseases is given. We observe that for a controlled domain, when one sub-network is coherent (Resp. incoherent) this involves automatically a coherent (Resp. incoherent) behavior of the other sub-network.