Effect of mobility in partially occupied complex networks

The collective dynamics of coupled oscillators has been well studied in fully occupied networks, but little attention has been paid to the case of partially occupied networks. We study this problem by a dynamic bipartite model and focus on the influence of population mobility. We find that when the density of occupied nodes is smaller than the percolation threshold ${\rho }_c$, the order parameter will show an effect of mobility with optimal value at a medium moving probability. Its mechanism can be revealed through three factors, i.e., the size of the largest component, the mixing degree in individual components, and the frequency of exchange information among components. When the density of occupied nodes is larger than ${\rho }_c$, the moving probability will act as a bifurcation parameter to synchronization. The effect of mobility also exists for other dynamics such as the epidemic spreading where the effect is shown through the number of infected agents.

Figure 1

(Color online) $R$ versus $p$ with network size $L=1000$ and average degree $⟨k⟩=6$, where the squares and circles represent the cases of $\rho =0.2$ and 0.3, respectively.

Figure 2

(Color online) The average size of the largest component $S_{\text{max}}$ and the average number of components $N_{com}$ in Fig. 1, where the squares and circles represent the cases with $\rho =0.2$ and 0.3, respectively.

Figure 3

(Color online) (a) How the exchanging information between two subnetworks influences $R$; see text for details. (b) How the mixing in a component influences $R$.

Figure 4

(a) ${\Omega }_i$ versus $p$ for $\epsilon =0.5$ and $\rho =0.4$; (b) ${\Omega }_i$ versus $\rho$ for $\epsilon =0.5$ and $p=0.01$; (c) ${\Omega }_i$ versus $\epsilon$ for $\rho =0.4$ and $p=0.01$.

Figure 5

(Color online) $I$ versus $p$ in the network used in Fig. 1.