Figure 7

Numerical simulation of Eqs. (3) and (6) for a nine-leaf star network with 512 different initial conditions \({\mathbf {R}}(0)\), each of which is close to the state \({\mathbf {R}}_n^{(9)}\) of a particular predicted asymptotic configuration with number \(n=0,\ldots ,511\). Panels (a) and (b) correspond to the sigmoid boundary function with \(\mu =0.01\) and the Heaviside step boundary function, respectively. The frequencies \((\omega _1, \ldots , \omega _8, \omega _0, \omega _9)\), written in ascending order, are equidistantly distributed in the interval [0.6, 1]. The states \({\mathbf {R}}(0)\) are chosen so that the initial distances \(|{\mathbf {R}}(0)-{\mathbf {R}}_n^{(9)}|\) shown in blue squares are the same for all configurations. The yellow dots show the values of the corresponding distances \(|{\mathbf {R}}(t)-{\mathbf {R}}_n^{(9)}|\) at time \(t=300\), and the red circles at time \(t=76{,}000\). Parameter values: \(\varepsilon = 0.001\), \(\tau _+ = 0.15\), \(\tau _-=0.3\), and \(\alpha = 1\).