Crashes, Recoveries, and `Core-shifts' in a Model of Evolving Networks

A model of an evolving network of interacting molecular species is shown to exhibit repeated rounds of crashes in which several species get rapidly depopulated, followed by recoveries. The network inevitably self-organizes into an autocatalytic structure, which consists of an irreducible `core' surrounded by a parasitic `periphery'. Crashes typically occur when the existing autocatalytic set becomes fragile and suffers a `core-shift', defined graph theoretically. The nature of the recovery after a crash, in particular the time of recovery, depends upon the organizational structure that survives the crash. The largest eigenvalue of the adjacency matrix of the graph is an important signal of network fragility or robustness.