Excitation and suppression of chimeric states in the multilayer network of oscillators with nonlocal coupling

Mean field phase synchronization between chimera states

“…Recent work on chimera states, which are paradigmatic for this balance, has, therefore, progressed from the study of individual networks to interacting networks. Chimeras were studied in multilayer networks of phase oscillators, 7,[11][12][13]16,19 Hindmarsh-Rose, 7,9,10,14,18 and FitzHugh-Nagumo 27 model neurons, as well as chaotic time-discrete maps. 8,15,17 It was shown that couplings between network layers can suppress or induce [7][8][9][10][11][14][15][16][17] chimera states in individual layers and that chimeras can be identical, almost identical, or distinct across different layers.…”

“…Chimeras were studied in multilayer networks of phase oscillators, 7,[11][12][13]16,19 Hindmarsh-Rose, 7,9,10,14,18 and FitzHugh-Nagumo 27 model neurons, as well as chaotic time-discrete maps. 8,15,17 It was shown that couplings between network layers can suppress or induce [7][8][9][10][11][14][15][16][17] chimera states in individual layers and that chimeras can be identical, almost identical, or distinct across different layers. 7,8,[11][12][13][14][15][16]18 Coupling delays [8][9][10] as well as parameter mismatches or structural differences across layers 7,9,11,[15][16][17] were found to play an important role in this multilayer setting.…”

“…6 Therefore, while chimera states were traditionally studied in one-layer networks, recent work deals with interactions of chimera states across coupled layers in multilayer networks. [7][8][9][10][11][12][13][14][15][16][17][18][19] In particular, it was shown in Ref. 12 that driver-response couplings between layers can induce socalled generalized synchronization, [20][21][22] where the state of the response layer becomes a unique function of the state of the driver layer.…”

“…While these findings on generalized synchronization between chimera states 12 are appealing from a theoretical point of view, their applicability might remain limited because this particular type of synchronization is difficult to detect. Moreover, previous work [7][8][9][10][11][12][13][14][15][16][17] focused on multiplex networks, for which the layers must have the same number of oscillators and the inter-layer coupling connects individual oscillators in a pairwise and ordered topology. These constraints exclude many types of real-world multilayer networks, which in general can have different numbers of nodes in each layer, thereby already ruling out a multiplex connection topology across layers.…”

“…Furthermore, the nodes in the network of one layer might not be directly connected to the nodes in the network of the other layer but instead to some macroscopic variable of the other network. We, therefore, use a more general approach than in previous work [7][8][9][10][11][12][13][14][15][16][17][18][19] and study two-layer networks with a different number of oscillators in each layer. For each layer, we use the classical setting of a ring network of non-locally coupled identical phase oscillators in a chimera state.…”