The effects of synaptic time delay on motifs of chemically coupled Rulkov model neurons

Given the importance of the network motifs, we consider a pair of Rulkov chaotic map neurons, reciprocally coupled via symmetrical chemical synapses with the time delay τ. For the inhibitory and excitatory synapses, the system dynamics is determined by the synaptic weight gc, synaptic gain parameter k, time delay τ and the external excitation σ. Due to chaotic nature of the map and synaptic model complexity, the appropriately averaged cross-correlation of membrane potentials represents a suitable numerical diagnostics to quantify mutual synchronization. Along with the expected phase and anti-phase synchronization regimes, we find the emergent phenomena that significantly influence the synchronization behavior.