Chimera states and synchronization behavior in multilayer memristive neural networks

Traveling chimera states for coupled pendula

“…Chimeric behavior can be found in a variety of models, among others Kuramoto networks [3], chemical oscillators [4], neural networks [5][6][7][8] or mechanical systems [9,10]. They have been observed for typical complex networks of oscillators [3][4][5][6][9][10][11][12][13], as well as for the small ones [14,15], or even pure analytical [16]. Recent studies on chimera death for coupled chaotic oscillators can be found in [17], while in [18] the authors discuss the chimeric phenomenon in non-locally coupled excitable systems.…”

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.…”

“…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. For the special case of bipartite networks in-phase, anti-phase and out-of-phase chimeras were observed.…”

“…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.…”

“…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.…”