Figure 2

Examples of single gain band structure as a function of the heterogeneity for the Fourier component corresponding to \(n=1\). The connectivity functions are given by (8) with (21), the averaged synaptic footprints are fixed as (27). In (a) the parameterized curves \(\Gamma _{1}\) in the invariant plane defined by means of (44) and (45) are shown for \(\tau =2\) and Set A (cf. Table 1). In (c) the corresponding growth rates (\(\operatorname{Re}\{\lambda _{1}^{\pm }\}\) in (43)) are shown as a function of the wave number k. In (b) the curves \(\Gamma _{1}\) are shown for \(\tau =4.4\) and Set B (cf. Table 1). The corresponding growth rates are shown in (d). The black bullet points • in (a) and (b) are the initial points of the curves \(\Gamma _{1}\), \(\eta =k^{2}=0\). The heterogeneity parameters producing the red, green, and blue curves are Set 2, Set 3, and Set 4 in Table 2, respectively. Zoomed black curves corresponding to Set 1 are presented in the separate figure, see (a) and (b) of Fig. 4