Figure 4

Asymptotic configurations for a two-leaf star network. (a–g) Predicted configurations. Solid arrows show the unidirectional coupling with maximum synaptic weight that results in synchronization between the leaf and the hub. Dashed arrows correspond to a weak synaptic connections, so the leaf is not synchronized with the hub. The required frequency inequality is indicated above each configuration. The two characters in brackets under each configuration represent its code. (h) Distributions of color-coded asymptotic values of coupling weights \(A_j\) and \(B_j\) for a two-leaf star network, obtained by integrating Eqs. (3) and (6). The results presented in three rows correspond to three different possibilities of the hub frequency to fall into different frequency intervals of the leaves: \(\omega _0<\omega _1\) (top row), \(\omega _1<\omega _0<\omega _2\) (middle row), and \(\omega _2<\omega _0\) (bottom row). The top row of (h) (from left to right) match configurations (g,b,e,a). For the middle and bottom rows, the corresponding configurations are, respectively, as follows: (g,d,e,c) and (g,d,f,c). All frequencies are taken from the array (0.55, 0.85, 1). The parameter \(\varepsilon =0.001\), and the parameter \(\mu = 0.01\) corresponds to the sigmoid boundary function (5). The values of the parameters \(\alpha\), \(\tau _+\) and \(\tau _-\) are the same as in Fig. 1.