Figure 1
The impact of a single autapse on synchronization in a toy neuronal network. (a1) Without any autapse, the network has four nodes and four edges, where each node is a Hindmarsh-Rose neuron. (b1–d1) Network structure when a single autapse (represented by the red curve with an arrow) is present at node 1, 2, and 4, respectively. (a2–d2) For the network structures in (a1–d1), respectively, the dynamical behaviors of the network in terms of synchronization. Shown in each panel is a plot of the x variable from each node versus the averaged value of this variable over all the nodes during the time evolution. When there is global synchronization, all the variables are equal to their average value at any instant of time, tracing out a straight line segment along the diagonal. Any deviation from the diagonal signifies lack of synchronization. The uniform coupling parameter is ε = 1 and the time delay associated with the autapse is τ = 4.
