Fig. 3

Transition lines. Behaviour along the dotted lines marked in Fig. 4, for N = 1600, κ_∞ = 10 and n = 5. a and c show \(\bar g\left( T \right)\) and \(\bar m\left( T \right)\), respectively, for different values of α, as indicated. b and d correspond, respectively, to \(\bar g\left( \alpha \right)\) and \(\bar m\left( \alpha \right)\), for different temperatures as indicated. Solid points are for homogeneous IC and empty ones for heterogeneous IC, in every panel. Notice that some isolines go through the three phases: for T = 1.0 and 1.1 (b and d) the system is initially in the homogeneous memory phase, and an increase in α leads through \(\alpha _c^m(T)\) to networks that are heterogeneous enough to maintain memory, which further increases heterogeneity due to the feedback loop (\(\bar g\left( \alpha \right)\) decreases). A final increase in α leads through \(\alpha _c^t(T)\) to heterogeneous networks. Similarly in a and c, the system visits for α = 1 the three phases: at very low T, α is high enough to develop heterogeneous memory networks, but a slight noise increase is enough to suppress heterogeneity, until noise is too high and memory is also lost, leading to the homogeneous noisy phase. Data points are averaged over 30 realizations and error bars correspond to s.d