Effect of topology upon relay synchronization in triplex neuronal networks

Drauschke, Fenja; Sawicki, Jakub; Berner, Rico; Omelchenko, Iryna; Schöll, Eckehard

doi:10.1063/5.0008341

Cited by 34 publications

(19 citation statements)

References 59 publications

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“…Recently, a prominent line of research emerged which studies chimera states in multilayer networks [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. Multilayer networks are important modelling tools for complex systems such as transportation networks, social interactions and the brain [58,59].…”

Section: Introductionmentioning

confidence: 99%

Remote pacemaker control of chimera states in multilayer networks of neurons

et al. 2020

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Networks of coupled nonlinear oscillators allow for the formation of nontrivial partially synchronized spatiotemporal patterns, such as chimera states, in which there are coexisting coherent (synchronized) and incoherent (desynchronized) domains. These complementary domains form spontaneously and it is impossible to predict where the synchronized group will be positioned within the network. Therefore, possible ways to control the spatial position of the coherent and incoherent groups forming the chimera states are of high current interest. In this work we investigate how to control chimera patterns in multiplex networks of FitzHugh-Nagumo neurons, and in particular we want to prove that it is possible to remotely control chimera states exploiting the multiplex structure. We introduce a pacemaker oscillator within the network: this is an oscillator that does not receive input from the rest of the network but is sending out information to its neighbours. The pacemakers can be positioned in one or both layers. Their presence breaks the spatial symmetry of the layer in which they are introduced and allows us to control the position of the incoherent domain. We demonstrate how the remote control is possible for both uni-and bidirectional coupling between the layers. Furthermore we show which are the limitations of our control mechanisms when it is generalized from single layer to multilayer networks.

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Section: Introductionmentioning

confidence: 99%

Remote pacemaker control of chimera states in multilayer networks of neurons

et al. 2020

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“…Recently the notion of relay synchronization has been extended from completely synchronized states to partial synchronization patterns in the individual layers of a three-layer multiplex network. It has been shown that the three-layer structure of the network allows for (partial) synchronization of chimera states in the outer layers via the relay layer [27][28][29][30][31]. Going towards more realistic models, time-delay plays an important role in the modeling of the dynamics of complex networks.…”

Section: Introductionmentioning

confidence: 99%

Influence of Sound on Empirical Brain Networks

Sawicki

Schöll

2021

Front. Appl. Math. Stat.

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We analyze the influence of an external sound source in a network of FitzHugh–Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report synchronization patterns, induced by the frequency of the sound source. We show that the level of synchrony can be enhanced by choosing the frequency of the sound source and its amplitude as control parameters for synchronization patterns. We discuss a minimum model elucidating the modalities of the influence of music on the human brain.

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“…Recently, relay synchronization has been illustrated in multi-layer and multiplex frameworks with different intra-layer topologies, such as Erdős-Rényi and scale-free [35]. In Reference [36], random inhomogeneities of the small-world type have been introduced in the network layers to scrutinize the robustness of relay synchronization. Continuous and discrete-time systems have been used as individual units to induce spatiotemporal structures in triplex networks [37,38].…”

Section: Introductionmentioning

confidence: 99%

Relay Synchronization in a Weighted Triplex Network

2021

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Relay synchronization in multi-layer networks implies inter-layer synchronization between two indirectly connected layers through a relay layer. In this work, we study the relay synchronization in a three-layer multiplex network by introducing degree-based weighting mechanisms. The mechanism of within-layer connectivity may be hubs-repelling or hubs-attracting whenever low-degree or high-degree nodes receive strong influence. We adjust the remote layers to hubs-attracting coupling, whereas the relay layer may be unweighted, hubs-repelling, or hubs-attracting network. We establish that relay synchronization is improved when the relay layer is hubs-repelling compared to the other cases. We determine analytically necessary stability conditions of relay synchronization state using the master stability function approach. Finally, we explore the relation between synchronization and the topological property of the relay layer. We find that a higher clustering coefficient hinders synchronizability, and vice versa. We also look into the intra-layer synchronization in the proposed weighted triplex network and establish that intra-layer synchronization occurs in a wider range when relay layer is hubs-attracting.

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Effect of topology upon relay synchronization in triplex neuronal networks

Cited by 34 publications

References 59 publications

Remote pacemaker control of chimera states in multilayer networks of neurons

Remote pacemaker control of chimera states in multilayer networks of neurons

Influence of Sound on Empirical Brain Networks

Relay Synchronization in a Weighted Triplex Network

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