Synchronization and chimera in a multiplex network of Hindmarsh-Rose neuron map with flux-controlled memristor

In network analysis, using discrete models, known as map models, brings advantages to the network since such models are more flexible and efficient than continuous ones. Memristor is another concept that brings a significant nonlinearity to the system. Therefore, different initially discrete or discretized memristive maps can be found in the literature. To benefit from the advantages of the memristive maps and to model different multi-level neural interactions, in this paper, we investigate the synchronization and chimera state in a multiplex network of discretized Hindmarsh-Rose maps with a flux-controlled memristor. The studied multiplex network was considered to have two layers, each having a different small-world structure with 50 neurons, and corresponding neurons from different layers were linked. In the constructed two-layer network, the influence of different intra-layer couplings on synchronization was studied, while chemical synapses were considered the only inter-layer neural interactions. We found that when intra-layer neurons interacted electrically, they could achieve synchronization as the electrical coupling strength increased. However, when neurons were linked through electrical and chemical couplings, they could not reach a synchronous state. Similarly, chemically coupled intra-layer neurons could not achieve synchronization as well. Also, we observed that chemical inter-layer interactions could lead to the formation of coherent and incoherent clusters. Thus, in a weak intra-layer coupling value, the chimera state was found by increasing the inter-layer coupling strength.