Figure 3
(a,b) The dependence of the oscillation proportion \({p}_{{\rm{os}}}\) (a) and the average path length (APL) of network \({d}_{{\rm{APL}}}\) (b) on the system size \(N\) for different node degrees \(k\) in EHRNs (shown by red dots for \(k\,=\,3\) and shown by blue squares for \(k\,=\,4\)). (c,d) The dependence of the oscillation proportion \({p}_{{\rm{os}}}\) (c) and the APL of network \({d}_{{\rm{APL}}}\) (d) on the node degree \(k\) for different system sizes \(N\) in EHRNs (shown by red dots for \(N\,=\,100\), shown by blue squares for \(N\,=\,400\), shown by green triangles for \(N\,=\,700\) and shown by pink diamonds for \(N\,=\,1000\)). System parameters are chosen as: \(a\,=\,0.90\), \(b\,=\,0.04\), \(\varepsilon \,=\,0.04\) and \(D\,=\,0.30\). The oscillation proportion is defined as \({p}_{{\rm{os}}}=\frac{{N}_{{\rm{os}}}}{{N}_{{\rm{ALL}}}}\). Here \({N}_{{\rm{ALL}}}\) is the total number of numerical simulations executed for each set of parameters, and \({N}_{{\rm{os}}}\) is the number of PSOs counted in the \({N}_{{\rm{ALL}}}\) independent numerical simulations. One hundred independent numerical simulations (i.e., \({N}_{{\rm{ALL}}}\mathrm{=100}\)) are performed for each set of parameters.
