Multilayer coevolution dynamics of the nonlinear voter model

Byungjoon Min; Maxi San Miguel

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Multilayer coevolution dynamics of the nonlinear voter model

Byungjoon Min, Maxi San Miguel

Adaptation and Self-Organizing Systems · Submitted 29 Nov 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In terms of these three parameters, p, q and ` we find a rich phase diagram with different phases and transitions.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.33 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.77 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We study a coevolving nonlinear voter model on a two-layer network. Coevolution stands for coupled dynamics of the state of the nodes and of the topology of the network in each layer. The plasticity parameter p measures the relative time scale of the evolution of the states of the nodes and the evolution of the network by link rewiring. Nonlinearity of the interactions is taken into account through a parameter q that describes the nonlinear effect of local majorities, being q = 1 the marginal situation of the ordinary voter model. Finally the connection between the two layers is measured by a degree of multiplexing `. In terms of these three parameters, p, q and ` we find a rich phase diagram with different phases and transitions. When the two layers have the same plasticity p, the fragmentation transition observed in a single layer is shifted to larger values of p plasticity, so that multiplexing avoids fragmentation. Different plasticities for the two layers lead to new phases that do not exist in a coevolving nonlinear voter model in a single layer, namely an asymmetric fragmented phase for q > 1 and an active shattered phase for q < 1. Coupling layers with dfferent types of nonlinearity, q1 < 1 and q2 > 1, we can find two different transitions by increasing the plasticity parameter, a first absorbing transition with no fragmentation and a subsequent fragmentation transition.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study a coevolving nonlinear voter model on a two-layer network.	contribution 0.99	0.92	0.03	asserted 0.93
s1	Coevolution stands for coupled dynamics of the state of the nodes and of the topology of the network in each layer.	background 0.76	0.08	0.03	asserted 1.00
s2	The plasticity parameter p measures the relative time scale of the evolution of the states of the nodes and the evolution of the network by link rewiring.	method 0.96	0.33	0.03	asserted 1.00
s3	Nonlinearity of the interactions is taken into account through a parameter q that describes the nonlinear effect of local majorities, being q = 1 the marginal situation of the ordinary voter model.	method 0.98	0.48	0.03	asserted 1.00
s4	Finally the connection between the two layers is measured by a degree of multiplexing `.	method 0.95	0.32	0.02	asserted 1.00
s5	In terms of these three parameters, p, q and ` we find a rich phase diagram with different phases and transitions.	result 0.79	0.95	0.18	asserted 1.00
s6	When the two layers have the same plasticity p, the fragmentation transition observed in a single layer is shifted to larger values of p plasticity, so that multiplexing avoids fragmentation.	result 0.99	0.89	0.23	asserted 1.00
s7	Different plasticities for the two layers lead to new phases that do not exist in a coevolving nonlinear voter model in a single layer, namely an asymmetric fragmented phase for q > 1 and an active shattered phase for q < 1.	result 1.00	0.89	0.25	asserted 1.00
s8	Coupling layers with dfferent types of nonlinearity, q1 < 1 and q2 > 1, we can find two different transitions by increasing the plasticity parameter, a first absorbing transition with no fragmentation and a subsequent fragmentation transition.	result 1.00	0.89	0.18	hedged possibility 0.65

What kind of paper the classifier reports this is: theoretical result 0.57 · evidence from simulation or computation 0.97.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

We study a coevolving nonlinear voter model on a two-layer network. Coevolution stands for coupled dynamics of the state of the nodes and of the topology of the network in each layer. The plasticity parameter p measures the relative time scale of the evolution of the states of the nodes and the evolution of the network by link rewiring. Nonlinearity of the interactions is taken into account through a parameter q that describes the nonlinear effect of local majorities, being q = 1 the marginal situation of the ordinary voter model. Finally the connection between the two layers is measured by a degree of multiplexing `. In terms of these three parameters, p, q and ` we find a rich phase diagram with different phases and transitions. When the two layers have the same plasticity p, the fragmentation transition observed in a single layer is shifted to larger values of p plasticity, so that multiplexing avoids fragmentation. Different plasticities for the two layers lead to new phases that do not exist in a coevolving nonlinear voter model in a single layer, namely an asymmetric fragmented phase for q > 1 and an active shattered phase for q < 1. Coupling layers with dfferent types of nonlinearity, q1 < 1 and q2 > 1, we can find two different transitions by increasing the plasticity parameter, a first absorbing transition with no fragmentation and a subsequent fragmentation transition.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites as background 1 paper

The concept of multilayer networks [ref] has been proposed along with interconnected networks [ref] , interdependent networks [ref] , and multiplex networks [ref] , for a more complete modeling of interconnected systems.

Percolation on interacting networks · Introduction · 0.98

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