Figure 4
From: A network-based microfoundation of Granovetter’s threshold model for social tipping
Bifurcation analysis and hysteresis of the refined Granovetter model with an emergent threshold distribution as given by the analytical approximation. (a) Smallest stable fixed point min(r*) for different shares of certainly acting \(a\) and potentially acting individuals \(p\). The black circle denotes a cusp-bifurcation. Black dashed horizontal/vertical lines correspond to the diagrams in (b,c) that show a saddle-node bifurcation. For (b–d), solid (dotted) lines indicate stable (unstable) fixed points r*. Grey shading indicates those areas where \({r}^{\ast }\notin [a,p]\) and that can thus not be reached. The yellow circled area in (a) indicates the bistable regime. Red dashed horizontal/vertical lines in (a) correspond to values of p and a at which no bifurcation is observed and thus r* varies smoothly in (b,c). (d) Shows the bifurcation diagram in the threshold fraction \(\rho \). Fixed parameters are: \(a=0.16\) for (c) (\(a=0.24\) for the red curve) and (d), \(p=0.67\) for (b) (\(p=0.58\) for the red curve) and (d), and \(\rho =0.4\) for (a–c).
