Ginzburg-Landau approximation for self-sustained oscillators weakly coupled on complex directed graphs

Patti, Francesca Di; Fanelli, Duccio; Miele, Filippo; Carletti, Timotéo

doi:10.1016/j.cnsns.2017.08.012

Cited by 14 publications

(7 citation statements)

References 22 publications

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“…However, the effectiveness of the latter method is exclusively limited to parameter values that are very close to the stability threshold. In this sense, our approach is more general, both from allowing a larger set of parameters where the method remains valid, and at the same time, it is independent of the choice of the model compared to previous works [ 33 ]. The passage to an autonomous system is also essential in explaining the effect of the imaginary part of the Laplacian eigenvalues in the newly obtained stability function, the dispersion relation.…”

Section: The Case Of Normal Directed Networkmentioning

confidence: 99%

Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality

Muolo

Carletti

Gleeson

et al. 2020

Entropy

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Synchronization is an important behavior that characterizes many natural and human made systems that are composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, with the latter being modeled by complex networks. The dynamical behavior of the system and the topology of the underlying network are strongly intertwined, raising the question of the optimal architecture that makes synchronization robust. The Master Stability Function (MSF) has been proposed and extensively studied as a generic framework for tackling synchronization problems. Using this method, it has been shown that, for a class of models, synchronization in strongly directed networks is robust to external perturbations. Recent findings indicate that many real-world networks are strongly directed, being potential candidates for optimal synchronization. Moreover, many empirical networks are also strongly non-normal. Inspired by this latter fact in this work, we address the role of the non-normality in the synchronization dynamics by pointing out that standard techniques, such as the MSF, may fail to predict the stability of synchronized states. We demonstrate that, due to a transient growth that is induced by the structure’s non-normality, the system might lose synchronization, contrary to the spectral prediction. These results lead to a trade-off between non-normality and directedness that should be properly considered when designing an optimal network, enhancing the robustness of synchronization.

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Section: The Case Of Normal Directed Networkmentioning

confidence: 99%

Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality

Muolo

Carletti

Gleeson

et al. 2020

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, the effectivity of the latter method is exclusively limited to parameters values very close to the stability threshold. In this sense, our approach is more general, both from allowing a larger set of parameters where the method remains valid, and at the same time, it is independent of the choice of the model compared to previous works [35]. The passage to an autonomous system is also essential in explaining the effect of the imaginary part of the Laplacian eigenvalues in the newly obtained stability function, the dispersion relation.…”

Section: A the Case Of Normal Directed Networkmentioning

confidence: 95%

Synchronization dynamics in non-normal networks: the trade-off for optimality

Muolo,

Carletti,

Gleeson

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, the latter being modeled by complex networks. The dynamical behavior of the system and the topology of the underlying network are strongly intertwined, raising the question of the optimal architecture that makes synchronization robust. The Master Stability Function (MSF) has been proposed and extensively studied as a generic framework to tackle synchronization problems. Using this method, it has been shown that for a class of models, synchronization in strongly directed networks is robust to external perturbations. In this paper, our approach is to transform the non-autonomous system of coupled oscillators into an autonomous one, showing that previous results are model-independent. Recent findings indicate that many real-world networks are strongly directed, being potential candidates for optimal synchronization. Inspired by the fact that highly directed networks are also strongly non-normal, in this work, we address the matter of non-normality by pointing out that standard techniques, such as the MSF, may fail in predicting the stability of synchronized behavior. These results lead to a trade-off between nonnormality and directedness that should be properly considered when designing an optimal network, enhancing the robustness of synchronization.

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“…Recently proposed analytical frameworks [7] can be very useful in this respect. Second, within the framework proposed here, where epidemics can be regarded as self-oscillators, it comes naturally the question of coupling and synchronization [27,28] of epidemic waves running on different networks that are weakly connected, e.g. by migration processes.…”

Section: J Stat Mech (2022) 013404mentioning

confidence: 99%

Epidemic oscillations induced by social network control

Caccioli¹,

Martino²

2022

J. Stat. Mech.

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Epidemic spreading can be suppressed by the introduction of containment measures such as social distancing and lockdowns. Yet, when such measures are relaxed, new epidemic waves and infection cycles may occur. Here we explore this issue in compartmentalized epidemic models on graphs in presence of a feedback between the infection state of the population and the structure of its social network for the case of discontinuous control. We show that in random graphs the effect of containment measures is simply captured by a renormalization of the effective infection rate that accounts for the change in the branching ratio of the network. In our simple setting, a piece-wise mean-field approximation can be used to derive analytical formulae for the number of epidemic waves and their length. A variant of the model with imperfect information is used to model data of the recent COVID-19 epidemics in the Basque Country and Lombardy, where we estimate the extent of social network disruption during lockdowns and characterize the dynamical trajectories in the phase space.

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Ginzburg-Landau approximation for self-sustained oscillators weakly coupled on complex directed graphs

Cited by 14 publications

References 22 publications

Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality

Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality

Synchronization dynamics in non-normal networks: the trade-off for optimality

Epidemic oscillations induced by social network control

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