Chimera States With 2D Deterministic and Random Fractal Connectivity - Argyropoulos, George; Provata, Astero (Frontiers in Applied Mathematics and Statistics, 2019)
We study the formation of chimera states in 2D lattices with hierarchical (fractal) connectivity. The dynamics of the nodes follow the Leaky Integrate-and-Fire model and the connectivity has the form of a deterministic or a random Sierpinski carpet. We provide numerical evidence that for deterministic fractal connectivity and small values of the coupling strength, a hierarchical incoherent spot is produced with internal structure influenced by the fractal connectivity scheme. The spot size is similar to the size of the coupling matrix. Stable spots can be formed for symmetric fractal connectivity, while travelling ones are found when the connectivity matrix is asymmetric with respect to the center. For fractal coupling schemes spiral wave chimeras are produced and curious stable patterns are reported, which present triple coexistence of coherent regions, incoherent domains and travelling waves. In all cases, the coherent domains demonstrate the lowest mean phase velocities $ω$, the incoherent domains show intermediate $ω$-velocities, while the travelling waves show the highest $ω$-values. These findings confirm previous studies on symmetric deterministic hierarchical connectivities and extend here to slanted and random fractals.