Figure 5

Example of a Turing type of bifurcation (56) for the Fourier component corresponding to \(n=1\). The connectivity functions are given by (8) and (21), the averaged synaptic footprints are fixed as (27). The parameterized curves \(\Gamma _{1}\) defined by means of (44) and (45) are shown for \(\tau =2\) for Set A (cf. Table 1). The black point • denotes the initial point of \(\Gamma _{1}\). The input heterogeneity parameter vector â is given as \(\hat{a}=(0.1,0.1,0.1)\) and \(\hat{\alpha }=\alpha _{ii}\). The red and the blue curve corresponds to \(\alpha _{ii}=0.29\) and \(\alpha _{ii}=0.31\), respectively. For \(\hat{\alpha }_{c}=0.3009\) (corresponding to the black curve), we have a Turing type of bifurcation