Nonlinearity + Networks: A 2020 Vision

Porter, Mason A.

doi:10.1007/978-3-030-44992-6_6

Cited by 35 publications

(18 citation statements)

References 166 publications

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“…Besides the paradigm of static networks the analysis of interconnected dynamical system on temporally evolving connectivity structures has become a future challenge in nonlinear science [POR19]. Here, two approaches have to be distinguished.…”

Section: Dynamics Of Complex Networkmentioning

confidence: 99%

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Berner¹

2021

Springer Theses

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Collective phenomena in systems of interconnected dynamical units are omnipresent in nature. The swarm behavior in flocks of birds or schools of fish, the synchronous flashing of fireflies or even coherent spiking of neurons in the human brain are just a few examples of collective motion. Elucidating the mechanisms that give rise to synchronization is crucial in order to understand biological self-organization. For this sake, the theory of dynamical networks has been successfully applied over the last decades to boil down the complex dynamics from natural systems to their essentials. In addition, dynamical networks with adaptive couplings and hence non-constant network structure appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. In this thesis, we study adaptive networks and their properties which give rise to the emergence of a variety of synchronization patterns, including complete and cluster synchronization as well as solitary and chimera-like states. One of the main fields of application that is investigated in this thesis concerns neuroscience. However, the methods and approaches developed in this work are not restricted to a specific field of application.aus gekoppelten Phasenoszillatoren an und zeigen, wie das subtile Zusammenspiel zwischen Adaptivität und Netzwerkstruktur die Entstehung komplexer partieller Synchronisationsmuster hervorruft.Trotz des regen Interesses an adaptiven Netzwerken ist über das Zusammenspiel adaptiv gekoppelter Netzwerkgruppen wenig bekannt. Solche adaptiven Mehrschicht-oder Multiplex-Netzwerke kommen in neuronalen Netzwerken ganz natürlich vor. Wir schlagen ein Konzept zur Erzeugung und Stabilisierung diverser partieller Synchronisationsmuster (Phasen-Cluster) in adaptiven Netzwerken vor. Wir zeigen, dass das "Multiplexen" verschiedene stabile Phasen-Cluster-Zustände induzieren kann, selbst wenn diese in den Einschicht-Systemen nicht stabil sind oder gar nicht existieren. Weiterhin entwickeln wir eine Methode zur Analyse von Laplace-Matrizen von Multiplex-Netzwerken, die einen Einblick in die spektrale Struktur dieser Netzwerke ermöglicht und damit eine Reduktion des Stabilitätsproblems auf die von Einschicht-Netzwerken ermöglicht. Wir setzen die neue Methode ein, um analytische Ergebnisse für die Stabilität der Zustände im Mehrschicht-System zu erhalten.

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Section: Dynamics Of Complex Networkmentioning

confidence: 99%

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Berner¹

2021

Springer Theses

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“…Recently, the role of complex contagion mechanisms (i.e., contagion processes that cannot be described solely by pairwise interactions) has received much attention. 16 It has been shown that higher-order interactions in networks (i.e., interactions involving multiple nodes) can have profound effects on dynamical network processes 17 such as opinion formation, 18 synchronization, 19–21 and population dynamics. 22 Efforts to map higher-order interactions in real-world networks have an uncovered rich structure, 23 which is only now starting to be appreciated.…”

Section: Introductionmentioning

confidence: 99%

The effect of heterogeneity on hypergraph contagion models

Landry

Restrepo

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

107

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The dynamics of network social contagion processes such as opinion formation and epidemic spreading are often mediated by interactions between multiple nodes. Previous results have shown that these higher-order interactions can profoundly modify the dynamics of contagion processes, resulting in bistability, hysteresis, and explosive transitions. In this paper, we present and analyze a hyperdegree-based mean-field description of the dynamics of the susceptible–infected–susceptible model on hypergraphs, i.e., networks with higher-order interactions, and illustrate its applicability with the example of a hypergraph where contagion is mediated by both links (pairwise interactions) and triangles (three-way interactions). We consider various models for the organization of link and triangle structures and different mechanisms of higher-order contagion and healing. We find that explosive transitions can be suppressed by heterogeneity in the link degree distribution when links and triangles are chosen independently or when link and triangle connections are positively correlated when compared to the uncorrelated case. We verify these results with microscopic simulations of the contagion process and with analytic predictions derived from the mean-field model. Our results show that the structure of higher-order interactions can have important effects on contagion processes on hypergraphs.

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“…Transcendental Information Cascades (TICs) are a method that first transforms any kind of sequential data into a network of recurring information tokens , to then exploit this network as a kind of analytical middle ground between views to the source data that would otherwise only be accessible individually through distinct analytical frameworks [16, 17]. The approach falls into the category of contemporary approaches that make use of network theory for the study of dynamical complex systems [4, 19, 21]. In the field of phylogenetic and phylogeographic analysis our approach can be compared to haplotype networks for example [1, 18] but with the benefit that the resulting network preserves access to temporal patterns at both macroscopic (e.g.…”

Section: Methodsmentioning

confidence: 99%

Networks of information token recurrences derived from genomic sequences may reveal hidden patterns in epidemic outbreaks: A case study of the 2019-nCoV coronavirus

Luczak‐Roesch

2020

Preprint

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Profiling the genetic evolution and dynamic spreading of viruses is a crucial task when responding to epidemic outbreaks. We aim to devise novel ways to model, visualise and analyse the temporal dynamics of epidemic outbreaks in order to help researchers and other people involved in crisis response to make well-informed and targeted decisions about from which geographical locations and time periods more genetic samples may be required to fully understand the outbreak. Our approach relies on the application of Transcendental Information Cascades to a set of temporally ordered nucleotide sequences, and we apply it to real-world data that was collected during the currently ongoing outbreak of the novel 2019-nCoV coronavirus. We assess information-theoretic and network-theoretic measures that characterise the resulting complex network and identify touching points and temporal pathways that are candidates for deeper investigation by geneticists and epidemiologists.

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Nonlinearity + Networks: A 2020 Vision

Cited by 35 publications

References 166 publications

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

The effect of heterogeneity on hypergraph contagion models

Networks of information token recurrences derived from genomic sequences may reveal hidden patterns in epidemic outbreaks: A case study of the 2019-nCoV coronavirus

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