Enhanced robustness of evolving systems with bipartite topology

Abstract

Evolving open systems, in which new entities are continually introduced and those turning unfit go extinct, exhibit a phase transition between a diverging phase, where the system size grows indefinitely, and a finite phase, where it remains bounded. We show that imposing a bipartite interaction topology alone leaves this transition unchanged when the two partitions are introduced with equal initial connectivity. In contrast, when the initial degrees are asymmetric, the robustness of the system is markedly enhanced such that the transition shifts to higher connectivity and the diverging phase persists even when both initial degrees individually exceed the critical point of the corresponding unstructured system. In addition, we find a re-entrant transition, i.e. a return to the diverging phase as asymmetry is increased while the initial degree of one of the partitions is fixed, making it lying entirely outside the original mean-field picture. An extended mean-field analysis identifies the origin of these effects such that in the asymmetric regime, a feedback between the bipartite handshaking constraint and different extinction rates drives the mean degree of emergent network far above the initially assigned connectivity. This degree elevation suppresses extinction probabilities across the community while simultaneously concentrating extinctions among recently introduced, low-degree nodes. The interplay of these two effects constitutes a simple and universal robustness mechanism for evolving systems with asymmetric bipartite structure.