Early fragmentation in the adaptive voter model on directed networks

Zschaler, Gerd; Böhme, Gesa A.; Seißinger, Michael; Huepe, Cristián; Groß, Thilo

doi:10.1103/physreve.85.046107

Cited by 57 publications

(60 citation statements)

References 36 publications

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“…As system dynamics often rely on the existence of active links connecting nodes of different states, the frozen phase either manifests itself in a globally polarized network (with all nodes carrying the same state) or a fragmented network (featuring two or more connected components that are polarized, whereas globally the network is not). Transitions to and between those absorbing states in adaptive networks have been dealt with using mean-field approximations or small perturbations of the fragmented state [15,18,30,31,32,33].…”

Section: Introductionmentioning

confidence: 99%

Detecting and describing dynamic equilibria in adaptive networks

Wieland

Parisi

Nunes

2012

Eur. Phys. J. Spec. Top.

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We review modeling attempts for the paradigmatic contact process (or SIS model) on adaptive networks. Elaborating on one particular proposed mechanism of topology change (rewiring) and its mean field analysis, we obtain a coarse-grained view of coevolving network topology in the stationary active phase of the system. Introducing an alternative framework applicable to a wide class of adaptive networks, active stationary states are detected, and an extended description of the resulting steady-state statistics is given for three different rewiring schemes. We find that slight modifications of the standard rewiring rule can result in either minuscule or drastic change of steady-state network topologies.

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Section: Introductionmentioning

confidence: 99%

Detecting and describing dynamic equilibria in adaptive networks

Wieland

Parisi

Nunes

2012

Eur. Phys. J. Spec. Top.

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“…Inspired by earlier research on directed networks [31,[33][34][35][36][37], we propose two algorithms to construct directed networks. One is a rewiring algorithm that can be applied to any existing undirected network to obtain a directed network with any given directionality, but each node has the same in-degree and out-degree as the original undirected network.…”

Section: Algorithm Descriptionmentioning

confidence: 99%

Nonconsensus opinion model on directed networks

Havlin

Stanley

et al. 2014

Phys. Rev. E

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Dynamic social opinion models have been widely studied on undirected networks, and most of them are based on spin interaction models that produce a consensus. In reality, however, many networks such as Twitter and the World Wide Web are directed and are composed of both unidirectional and bidirectional links. Moreover, from choosing a coffee brand to deciding who to vote for in an election, two or more competing opinions often coexist. In response to this ubiquity of directed networks and the coexistence of two or more opinions in decision-making situations, we study a nonconsensus opinion model introduced by Shao et al. [Phys. Rev. Lett. 103, 018701 (2009)] on directed networks. We define directionality ξ as the percentage of unidirectional links in a network, and we use the linear correlation coefficient ρ between the in-degree and out-degree of a node to quantify the relation between the in-degree and out-degree. We introduce two degree-preserving rewiring approaches which allow us to construct directed networks that can have a broad range of possible combinations of directionality ξ and linear correlation coefficient ρ and to study how ξ and ρ impact opinion competitions. We find that, as the directionality ξ or the in-degree and out-degree correlation ρ increases, the majority opinion becomes more dominant and the minority opinion's ability to survive is lowered.

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“…In this chapter we present a novel approach, which allows for a precise analytical estimation of fragmentation thresholds. A major part of the described methods and applications was published in [115][116][117][118].…”

Section: Fragmentation Transitions In Models For Opinion Formationmentioning

confidence: 99%

Emergence and persistence of diversity in complex networks

Böhme

2013

Eur. Phys. J. Spec. Top.

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Complex networks are employed as a mathematical description of complex systems in many different fields, ranging from biology to sociology, economy and ecology. Dynamical processes in these systems often display phase transitions, where the dynamics of the system changes qualitatively. In combination with these phase transitions certain components of the system might irretrievably go extinct. In this case, we talk about absorbing transitions. Developing mathematical tools, which allow for an analysis and prediction of the observed phase transitions is crucial for the investigation of complex networks.In this thesis, we investigate absorbing transitions in dynamical networks, where a certain amount of diversity is lost. In some real-world examples, e.g. in the evolution of human societies or of ecological systems, it is desirable to maintain a high degree of diversity, whereas in others, e.g. in epidemic spreading, the diversity of diseases is worthwhile to confine. An understanding of the underlying mechanisms for emergence and persistence of diversity in complex systems is therefore essential. Within the scope of two different network models, we develop an analytical approach, which can be used to estimate the prerequisites for diversity.In the first part, we study a model for opinion formation in human societies. In this model, regimes of low diversity and regimes of high diversity are separated by a fragmentation transition, where the network breaks into disconnected components, corresponding to different opinions. We propose an approach for the estimation of the fragmentation point. The approach is based on a linear stability analysis of the fragmented state close to the phase transition and yields much more accurate results compared to conventional methods.In the second part, we study a model for the formation of complex food webs. We calculate and analyze coexistence conditions for several types of species in ecological communities. To this aim, we employ an approach which involves an iterative stability analysis of the equilibrium with respect to the arrival of a new species. The proposed formalism allows for a direct calculation of coexistence ranges and thus facilitates a systematic analysis of persistence conditions for food webs.In summary, we present a general mathematical framework for the calculation of absorbing phase transitions in complex networks, which is based on concepts from percolation theory. While the specific implementation of the formalism differs from model to model, the basic principle remains applicable to a wide range of different models.

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Early fragmentation in the adaptive voter model on directed networks

Cited by 57 publications

References 36 publications

Detecting and describing dynamic equilibria in adaptive networks

Detecting and describing dynamic equilibria in adaptive networks

Nonconsensus opinion model on directed networks

Emergence and persistence of diversity in complex networks

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