The simplest multilayer network of Rulkov neuron maps: A dynamical analysis under different neuronal interactions

Dynamical map-based networks have been considered in many scientific fields due to their exciting behaviors while they are of low computational costs and more flexibility. Hence, map-based neuronal networks can be preferable for studying the behavior of brain neurons due to their speed and simplicity. Synchronization, cluster synchronization, and chimera are three essential collective behaviors of neurons that have been noticed in many studies. The simplest multilayer neuronal network, capable of exhibiting synchronization, cluster synchronization, and chimera, is a two-layer network with two neurons in each layer. Considering the dynamics of the Rulkov map as the nodes' dynamics of the two-layer network, this paper aims to detect the regions of different collective behaviors of the network under different types of intralayer interactions: chemical synapses, electrochemical synapses, electrical synapses, and inner linking functions. In all cases, the interlayer neurons interact through chemical synapses. It is revealed that the considered network can exhibit different neuronal collective behaviors, such as complete synchronization, cluster synchronization, chimera, and asynchronization.