Memory decay and loss of criticality in quorum percolation
Résumé
In this paper, we present the effects of memory decay on a bootstrap percolation model applied to randomdirected graphs (quorum percolation). The addition of decay was motivated by its natural occurrence in physicalsystems previously described by percolation theory, such as cultured neuronal networks, where decay originatesfrom ionic leakage through the membrane of neurons and/or synaptic depression. Surprisingly, this featurealone appears to change the critical behavior of the percolation transition, where discontinuities are replacedby steep but finite slopes. Using different numerical approaches, we show evidence for this qualitative changeeven for very small decay values. In experiments where the steepest slopes can not be resolved and still appearas discontinuities, decay produces nonetheless a quantitative difference on the location of the apparent criticalpoint. We discuss how this shift impacts network connectivity previously estimated without considering decay.In addition to this particular example, we believe that other percolation models are worth reinvestigating, takinginto account similar sorts of memory decay.