Non-normal amplification of stochastic quasicycles

Nicoletti, Sara; Zagli, Niccolò; Fanelli, Duccio; Livi, Roberto; Carletti, Timotéo; Innocenti, Giacomo

doi:10.1103/physreve.98.032214

Cited by 11 publications

(13 citation statements)

References 31 publications

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“…Another aspect that is unavoidably associated with the high asymmetry of real networks is their non-normality [ 13 ], namely their adjacency matrix

satisfies the condition

[ 12 ]. The non-normality can be critical for the dynamics of networked systems [ 13 , 14 , 15 , 16 , 17 , 18 ]. In fact, in the non-normal dynamics regime, a finite perturbation regarding a stable state can undergo a transient instability [ 12 ], which, because of the nonlinearities, could never be reabsorbed [ 13 , 14 ].…”

Section: Introductionmentioning

confidence: 99%

“…The effect of non-normality in dynamical systems has been studied in several contexts, such as hydrodynamics [ 19 ], ecosystems stability [ 20 ], pattern formation [ 21 ], chemical reactions [ 22 ], etc. However, it is only recently that the ubiquity of non-normal networks and the related dynamics have been put to the fore [ 13 , 14 , 15 , 16 , 17 , 18 ]. In this paper, we will elaborate on these lines showing the impact of non-normality on the stability of a synchronous state.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Another aspect that is unavoidably associated with the high asymmetry of real networks is their non-normality [ 13 ], namely their adjacency matrix

satisfies the condition

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

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

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“…Non-normal networks appear ubiquitous, with strong non-normality having been found in food webs, transport, and biological, social, communication, and citation networks (22). In addition, we mention that, besides information transfer, non-normality turns out to be the key to explaining and understanding a variety of other equally important phenomena, for instance, the process of pattern formation in natural and biological systems (21,35), the selective amplification of cortical activity patterns in the brain (32), and the emergence of giant oscillations in noise-driven dynamical systems (36)(37)(38).…”

Section: Discussionmentioning

confidence: 99%

Efficient communication over complex dynamical networks: The role of matrix non-normality

et al. 2020

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In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media requires understanding of how they propagate and transform information in the face of noise. Here, we develop a framework that enables us to examine how network structure, noise, and interference between consecutive packets jointly determine transmission performance in complex networks governed by linear dynamics. Mathematically, normal networks, which can be decomposed into separate low-dimensional information channels, suffer greatly from readout noise. Most details of their wiring have no impact on transmission quality. Non-normal networks, however, can largely cancel the effect of noise by transiently amplifying select input dimensions while ignoring others, resulting in higher net information throughput. Our theory could inform the design of new communication networks, as well as the optimal use of existing ones.

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“…It is well known that non-normality amplifies transient dynamics [27,28,29] and may lead to convective instability [20]. Here the presence of noise makes this amplification perpetual [18].…”

Section: Linear Amplification Mechanismmentioning

confidence: 99%

Desynchronization and pattern formation in a noisy feed-forward oscillator network

et al. 2019

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We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is studied in a region of the parameters that would yield deterministic synchronization. Non normal directed couplings seed a coherent amplification of the perturbation: this latter manifests as a modulation, transversal to the limit cycle, which gains in potency node after node. If the lattice extends long enough, the initial synchrony gets eventually lost and the system moves toward a non trivial attractor, which can be analytically characterized as an asymptotic splay state. The noise assisted instability, ultimately vehiculated and amplified by the non normal nature of the imposed couplings, eventually destabilizes also this second attractor. This phenomenon yields spatiotemporal patterns, which cannot be anticipated by a conventional linear stability analysis. arXiv:1810.01933v1 [cond-mat.dis-nn]

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Non-normal amplification of stochastic quasicycles

Cited by 11 publications

References 31 publications

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

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

Efficient communication over complex dynamical networks: The role of matrix non-normality

Desynchronization and pattern formation in a noisy feed-forward oscillator network

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