Networks beyond pairwise interactions: Structure and dynamics

Physics Reports, Journal Year: 2020, Volume and Issue: 874, P. 1 - 92

Published: June 13, 2020

The complexity of many biological, social and technological systems stems from the richness interactions among their units. Over past decades, a great variety complex has been successfully described as networks whose interacting pairs nodes are connected by links. Yet, in face-to-face human communication, chemical reactions ecological systems, can occur groups three or more cannot be simply just terms simple dyads. Until recently, little attention devoted to higher-order architecture real systems. However, mounting body evidence is showing that taking structure these into account greatly enhance our modeling capacities help us understand predict emerging dynamical behaviors. Here, we present complete overview field beyond pairwise interactions. We first discuss methods represent give unified presentation different frameworks used describe highlighting links between existing concepts representations. review measures designed characterize models proposed literature generate synthetic structures, such random growing simplicial complexes, bipartite graphs hypergraphs. introduce rapidly research on topology. focus novel emergent phenomena characterizing landmark processes, diffusion, spreading, synchronization games, when extended elucidate relations topology properties, conclude with summary empirical applications, providing an outlook current conceptual frontiers.

Language: Английский

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Non-reciprocal phase transitions

Nature, Journal Year: 2021, Volume and Issue: 592(7854), P. 363 - 369

Published: April 14, 2021

Language: Английский

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The multiscale physics of cilia and flagella

Nature Reviews Physics, Journal Year: 2020, Volume and Issue: 2(2), P. 74 - 88

Published: Jan. 3, 2020

Language: Английский

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What Are Higher-Order Networks?

SIAM Review, Journal Year: 2023, Volume and Issue: 65(3), P. 686 - 731

Published: Aug. 1, 2023

Network-based modeling of complex systems and data using the language graphs has become an essential topic across a range different disciplines. Arguably, this graph-based perspective derives its success from relative simplicity graphs: A graph consists nothing more than set vertices edges, describing relationships between pairs such vertices. This simple combinatorial structure makes interpretable flexible tools. The as system models, however, been scrutinized in literature recently. Specifically, it argued variety angles that there is need for higher-order networks, which go beyond paradigm pairwise relationships, encapsulated by graphs. In survey article we take stock these recent developments. Our goals are to clarify (i) what networks are, (ii) why interesting objects study, (iii) how they can be used applications.

Language: Английский

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Metastable oscillatory modes emerge from synchronization in the brain spacetime connectome

Communications Physics, Journal Year: 2022, Volume and Issue: 5(1)

Published: July 15, 2022

Abstract A rich repertoire of oscillatory signals is detected from human brains with electro- and magnetoencephalography (EEG/MEG). However, the principles underwriting coherent oscillations their link neural activity remain under debate. Here, we revisit mechanistic hypothesis that transient brain rhythms are a signature metastable synchronization, occurring at reduced collective frequencies due to delays between areas. We consider system damped oscillators in presence background noise – approximating short-lived gamma-frequency generated within neuronal circuits coupled according diffusion weighted tractography Varying global coupling strength conduction speed, identify critical regime where spatially spectrally resolved modes (MOMs) emerge sub-gamma frequencies, MEG power spectra 89 healthy individuals rest. Further, demonstrate frequency, duration, scale MOMs as well frequency-specific envelope functional connectivity can be controlled by parameters, while connectome structure remains unchanged. Grounded physics delay-coupled oscillators, these numerical analyses how interactions locally fast spacetime lead emergence organized space time.

Language: Английский

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Adaptive dynamical networks

Physics Reports, Journal Year: 2023, Volume and Issue: 1031, P. 1 - 59

Published: Aug. 1, 2023

Language: Английский

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Network dynamics of coupled oscillators and phase reduction techniques

Physics Reports, Journal Year: 2019, Volume and Issue: 819, P. 1 - 105

Published: June 25, 2019

Investigating the dynamics of a network oscillatory systems is timely and urgent topic. Phase synchronization has proven paradigmatic to study emergent collective behavior within network. Defining phase dynamics, however, not trivial task. The literature provides an arsenal solutions, but results are scattered their formulation far from standardized. Here, we present, in unified language, catalogue popular techniques for deriving coupled oscillators. Traditionally, approaches reduction address (weakly) perturbed oscillator. They fall into three classes. (i) Many start off with Hopf normal form description, thereby providing mathematical rigor. There, caveat first derive proper form. We explicate several ways do that, both analytically (semi-)numerically. (ii) Other analytic capitalize on time scale separation and/or averaging over cyclic variables. While appealing more intuitive implementation, they often lack accuracy. (iii) Direct numerical help identify may limit overarching view how reduced depends model parameters. After illustrating reviewing necessary details single oscillators, turn networks oscillators as central issue this report. show detail concepts can be extended applied oscillator networks. Again, distinguish between techniques. As latter dwell form, also discuss associated methods. To illustrate benefits pitfalls different techniques, apply them point-by-point two classic examples: Brusselators elaborate Wilson–Cowan complex crucial analyses so analytical estimates prediction. most common towards that have successful describing only transition incoherence global synchronization, predicting existence less states. these predictions been confirmed experiments. show, large extent employed technique. In current future trends, provide overview various methods augmented well phase–amplitude reduction. Weindicate and, hence, allow improved derivation

Language: Английский

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FitzHugh–Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2020, Volume and Issue: 30(12)

Published: Dec. 1, 2020

We study patterns of partial synchronization in a network FitzHugh-Nagumo oscillators with empirical structural connectivity measured human subjects. report the spontaneous occurrence phenomena that closely resemble ones seen during epileptic seizures humans. In order to obtain deeper insights into interplay between dynamics and topology, we perform long-term simulations oscillatory on different paradigmatic structures: random networks, regular nonlocally coupled ring networks fractal connectivities, small-world various rewiring probability. Among these intermediate probability best mimics findings achieved using connectivity. For other topologies, either no spontaneously occurring epileptic-seizure-related can be observed simulated dynamics, or overall degree remains high throughout simulation. This indicates topology some balance regularity randomness favors self-initiation self-termination episodes seizure-like strong synchronization.

Language: Английский

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A universal route to explosive phenomena

Science Advances, Journal Year: 2021, Volume and Issue: 7(16)

Published: April 16, 2021

The emergence of discontinuous critical transitions can typically be expected when an additional feature is added to a system.

Language: Английский

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Desynchronization Transitions in Adaptive Networks

Physical Review Letters, Journal Year: 2021, Volume and Issue: 126(2)

Published: Jan. 15, 2021

Adaptive networks change their connectivity with time, depending on dynamical state. While synchronization in structurally static has been studied extensively, this problem is much more challenging for adaptive networks. In Letter, we develop the master stability approach a large class of This allows reducing to low-dimensional system, by decoupling topological and properties. We show how interplay between adaptivity network structure gives rise formation islands. Moreover, report desynchronization transition emergence complex partial patterns induced an increasing overall coupling strength. illustrate our findings using coupled phase oscillators FitzHugh-Nagumo neurons synaptic plasticity.

Language: Английский

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