Recombining monogamous populations: Epidemics and chaotic synchronization

I consider agent populations on networks where, at any given time, each node is connected to just one neighbour. The lack of connectivity in the instantaneous interaction pattern of these "monogamous" populations -that would prevent the emergence of any form of collective behaviour- is compensated by occasional random reconnections which recombine interacting couples by exchanging their partners. On these dynamic interaction patterns, I analyze the critical transitions (a) to endemic states in an SIS epidemiological model, and (b) to full synchronization in an ensemble of coupled chaotic maps. The two transitions are recovered if the recombination rate is sufficiently large, thus giving rise to a bifurcation as this rate varies. This new critical phenomenon is characterized both analytically and numerically.

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