Figure 6

Results of three leaf star modeling. (a) Distributions of color-coded asymptotic values of coupling weights \(A_j\) and \(B_j\) for a three-leaf star network, obtained by integrating Eqs. (3) and (6) with different initial conditions. The leaves natural frequencies are \((\omega _1, \omega _2, \omega _3)\) = (0.55, 0.7, 1). The hub natural frequency \(\omega _0=0.85\) satisfies the inequality \(\omega _2<\omega _0<\omega _3\). The resulting distributions are labeled with codes that agree with the theoretically predicted asymptotic configurations shown in the third column of Table 1. (b) Probability distribution of eight different asymptotic configurations for a three-leaf star network, when the hub frequency is in the interval between the frequencies of the second and third leaves, \(\omega _2<\omega _0<\omega _3\). In panel (a), the configurations are numbered according to the decimal representation of the binary codes shown above each pattern in panel (a) (see main text for details). The distribution is constructed using 1000 randomly selected initial conditions for Eqs. (3) and (6). The initial values of the weights \(A_j\) and \(B_j\) were randomly and independently taken from the uniform distribution \([0, \alpha ]\).