Synchronization in delayed multiplex networks

Singh, Aradhana; Ghosh, Saptarshi; Jalan, Sarika; Kurths, Jürgen

doi:10.1209/0295-5075/111/30010

Cited by 35 publications

(25 citation statements)

References 49 publications

(55 reference statements)

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“…For instance, in the case of the multilayer brain network, physical connections may be adjustable while the manipulation of the functional connectivity is much more complicated. Although the phenomenon of synchronization 30,[38][39][40][41] and formation of partial synchronization patterns [28][29][30][31]33,34,[42][43][44] have been recently considered in multilayer networks, the challenging problem of controlling chimeras by weak multiplexing, in particular, in neuronal networks has not been yet investigated.…”

Section: Introductionmentioning

confidence: 99%

Weak multiplexing in neural networks: Switching between chimera and solitary states

Mikhaylenko

Ramlow

Jalan

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate spatio-temporal patterns occurring in a two-layer multiplex network of oscillatory FitzHugh-Nagumo neurons, where each layer is represented by a nonlocally coupled ring. We show that weak multiplexing, i.e., when the coupling between the layers is smaller than that within the layers, can have a significant impact on the dynamics of the neural network. We develop control strategies based on weak multiplexing and demonstrate how the desired state in one layer can be achieved without manipulating its parameters, but only by adjusting the other layer. We find that for coupling range mismatch weak multiplexing leads to the appearance of chimera states with different shapes of the mean velocity profile for parameter ranges where they do not exist in isolation. Moreover, we show that introducing a coupling strength mismatch between the layers can suppress chimera states with one incoherent domain (one-headed chimeras) and induce various other regimes such as in-phase synchronization or two-headed chimeras. Interestingly, small intra-layer coupling strength mismatch allows to achieve solitary states throughout the whole network.In nonlinear dynamics the paradigmatic FitzHugh-Nagumo (FHN) system is used to model the behavior of neurons. A single-layer network of nonlocally coupled oscillatory FHN neurons demonstrates various dynamic regimes including chimera states, that represent an intriguing mechanism of transition from complete coherence to complete incoherence. Here, we focus on a two-layer multiplex network and develop the tools for controlling the spatio-temporal patterns in the presence of weak coupling between the layers, i.e. weak multiplexing. We show that multiplexing combined with a mismatch between the layers, allows to induce chimera states in networks, where they do not appear in isolation. Our control also works in the opposite direction leading to the suppression of chimera states. Interestingly, small mismatch in the intra-layer coupling strength results in the formation of solitary states, that offer, compared to chimera states, an alternative scenario of transition from coherence to incoherence. Since multilayer structures naturally occur in neural networks (e.g., brain networks), we expect that our results can be useful for understanding and controlling of biological networks.

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Section: Introductionmentioning

confidence: 99%

Weak multiplexing in neural networks: Switching between chimera and solitary states

Mikhaylenko

Ramlow

Jalan

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…This is important from the point of view of engineering and brain surgery since it is not always possible to directly access the desired layer, while the network with which this layer is multiplexed may be accessible and adaptable. The multiplexing of networks has been shown to control many dynamical behaviors including synchronization [33][34][35][36][37] and pattern formation [38][39][40][41][42][43][44]. However, the control of CR based on the multiplexing of networks has not been extensively investigated.…”

Section: Introductionmentioning

confidence: 99%

Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network

Yamakou

Jost

2019

Phys. Rev. E

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We consider a two-layer multiplex network of diffusively coupled FitzHugh-Nagumo (FHN) neurons in the excitable regime. We show that the phenomenon of coherence resonance (CR) in one layer cannot only be controlled by the network topology, the intra and inter-layer time-delayed couplings, but also by another phenomenon, namely, self-induced stochastic resonance (SISR) in the other layer. Numerical computations show that when the layers are isolated, each of these noise-induced phenomena is weakened (strengthened) by a sparser (denser) ring network topology, stronger (weaker) intra-layer coupling forces, and longer (shorter) intra-layer time delays. However, CR shows a much higher sensitivity than SISR to changes in these control parameters. It is also shown, in contrast to SISR in a single isolated FHN neuron, that the maximum noise amplitude at which SISR occurs in the network of coupled FHN neurons is controllable, especially in the regime of strong coupling forces and long time delays. In order to use SISR in the first layer of the multiplex network to control CR in the second layer, we first choose the control parameters of the second layer in isolation such that in one case CR is poor and in another case, non-existent. It is then shown that a pronounced SISR cannot only significantly improve a poor CR, but can also induce a pro-

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“…top of the multiplex frameworks [26][27][28][29][30]. Of late, the emergence of ES has been shown in the multilayer networks comprised of Kuramoto oscillators as well as second-order Kuramoto oscillators [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Delay regulated explosive synchronization in multiplex networks

Kachhvah

Jalan

2019

New J. Phys.

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It is known that explosive synchronization (ES) in an isolated network of Kuramoto oscillators with inertia is significantly enhanced by the presence of time delay. Here we show that time delay in one layer of the multiplex network governs the transition to synchronization and ES in the other layers. We found that a single layer with time-delayed intra-layer coupling may experience a different type of transition to synchronization, e.g. ES or continuous, depending on the values of time delay. Importantly, the same type of transition is incorporated simultaneously in other layer(s) as well, irrespective of the intra-layer delay values. Hence, a suitable choice of time-delay in only one layer of a multiplex network can lead to a desired (either ES or continuous) transition simultaneously in the other layers, either directly or remotely connected to the delayed layer. These results offer a platform for a better understanding of the dynamics of those complex systems which are represented by the multilayered framework and contain time delays in the communication processes.

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Synchronization in delayed multiplex networks

Cited by 35 publications

References 49 publications

Weak multiplexing in neural networks: Switching between chimera and solitary states

Weak multiplexing in neural networks: Switching between chimera and solitary states

Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network

Delay regulated explosive synchronization in multiplex networks

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