Figure 3
A simplified HR model with diffusive coupling Eqs. (2)–(3) on a small graph illustrates the ubiquity of fractal basin structure of chimera states. (a) A network of 6 nodes that does not contain non-trivial symmetries. Nonetheless, there are many stable chimera states (at least on the time scale examined), and the basin structure shown in 8 colors indicates distinct patterns that can be derived by VPS structure, Eq. (8), by the same method as in Fig. 2. (b) Fractal basins for HR oscillators on this network when \(x_R=-0.5(1+\sqrt{5}), I=3.27, r=0.017, \sigma =0.0004\), and \(\beta =1\). All other \(x_i, y_i\), and \(z_i\) values at \(t=0\) are initialized to be \(-0.5\). (c) and (d) are zoomed regions indicated by the black rectangles in (b) and (c). (e) Centroid locations of two of the clusters in \(\tau -L\) space, which resembles the approximate form of most of (or all) VPSs inside (see SI (Sec. 2.6) for a detailed view of all \(e_l\) vectors inside each cluster).
