Figure 8

Networks of three nodes: escape times. Escape time, ℰ[τ], against connection strength, β, for the 13 different three-node networks depicted in Figure 7, with λ = 0.9 and α = 0.05. As β → 0, the escape times for all networks converge to a common value since in this limit all networks become equivalent to the fully disconnected network. In the other direction, as β → ∞, we find that there are groups of networks whose escape times appear to converge to a common value for the group. These groups are labelled (a-e) corresponding to the similarly labelled groups in Fig. 7, and in each case an example network from the group is depicted alongside the label. It appears that there is in some sense an equivalence between the networks within each of these groups that manifests in common behaviour when the connection strength is strong. For intermediate value of β (~ 0.01-1.0), the escape time moves smoothly between its value at the two extremes, for most networks. The exception is network 1 (group (a) which has the lowest escape time for β <~ 2.0, but a higher value for β >~ 2.0. This is due to the fact that this network has a disconnected first component. For this particular network, the qualitative behaviour depends on the general parametrisation of the system. The fully connected network (network 13) has the highest escape time for all values of β.