Figure 6
Networks of two nodes. (a) Presenting the three topologically distinct networks consisting of two nodes. A two-node network may either be fully disconnected, weakly connected or fully connected. (b) Escape time ℰ[τ] as a function of β for the three different two-node networks. (c) Reduced phase space for the disconnected two-node network (depicted top middle), with λ = 0.5 and β = 0.1. This space is spanned by r A and r B , the Cartesian distance of the state of each node (z A and z B ), from the fixed point. Quiver arrows show the direction and magnitude of the vector field within this space. Circles show attracting fixed points within this space. Outset plots show timeseries of the full system (with ω = 20) corresponding to the fixed points (circles) of the reduced space (x A and x B are displaced vertically for clarity). The solid lines mark the boundaries of the basins of attraction of the fixed points. The dotted line shows a noise-driven trajectory in the full space with α = 0.2 and initial condition z A = z B = 0. The lower-left circle is the origin of the full space which is a fixed point. The other three circles correspond to attracting limit-cycles, in which either one or both of the nodes is at the limit-cycle. (d) Reduced phase space for the weakly connected two-node network (depicted top middle). (e) Networks of two nodes: fully connected network. Presenting the reduced phase space for the fully connected two-node network (depicted top middle).