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Fig. 4.5 a An example random network with N = 100 nodes, and each node connects to other
nodes with the same degree k = 3. (b–c): The spatiotemporal evolution patterns of two different
oscillatory states in the same network shown in (a) by starting from different initial conditions. Both
patterns display the evolution of local variable u. The nodes are spatially arranged according to their
indexes i. (d) The DPAD structure corresponding to the oscillation state in (b), where a loop and
multiple chains are identified; e The DPAD structure corresponding to the oscillation state in (c),
where two independent subgraphs are found with each subgraph containing a loop and numerous
chains. (Adapted from Ref. [63])
4.3.4.2 Minimum Winfree Loop and Self-sustained Oscillations
Studies on the emergence of self-sustained oscillations in excitable networks indicate that regular self-sustained oscillations can emerge. However, whether there is
intrinsic mechanism in determining the oscillations in networks is still unclear. For
example, for Erdos–Renyi (ER) networks, whether the connection probability is
related to sustained oscillations is an open topic.