A Veritable Zoology of Successive Phase Transitions in the Asymmetric q-Voter Model on Multiplex Networks

Chmiel, Anna; Sienkiewicz, Julian; Fronczak, Agata; Fronczak, Piotr

doi:10.3390/e22091018

Cited by 19 publications

(16 citation statements)

References 40 publications

(76 reference statements)

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“…However, it has been reported that the hysteresis appears in real social systems 1 – 5 , which means that this issue is important also from the social point of view. Because hysteresis cannot appear within the continuous phase transition, researchers working in the field of opinion dynamics try to determine conditions under which discontinuous phase transitions appear 6 – 14 .…”

Section: Introductionmentioning

confidence: 99%

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

Nowak

Stoń

Sznajd-Weron

2021

Sci Rep

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We introduce a generalized version of the noisy q-voter model, one of the most popular opinion dynamics models, in which voters can be in one of $$s \ge 2$$ s ≥ 2 states. As in the original binary q-voter model, which corresponds to $$s=2$$ s = 2 , at each update randomly selected voter can conform to its q randomly chosen neighbors only if they are all in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act independently with probability p and with complementary probability $$1-p$$ 1 - p conform to others, and (2) quenched, which means that there is a fraction p of all voters, which are permanently independent and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo simulations. We show that for the number of states $$s>2$$ s > 2 the model displays discontinuous phase transitions for any $$q>1$$ q > 1 , on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for $$q>5$$ q > 5 . Moreover, unlike the case of $$s=2$$ s = 2 , for $$s>2$$ s > 2 discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one.

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Section: Introductionmentioning

confidence: 99%

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

Nowak

Stoń

Sznajd-Weron

2021

Sci Rep

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“…In the first layer, we leveraged the q -voter model, which many scholars have studied extensively [ 33 , 40 , 41 , 42 , 43 ]. In our context, this assumes that each agent i has an opinion respecting the current restrictions, given by a binary variable:

.…”

Section: Methodsmentioning

confidence: 99%

“…Although it is a straightforward model, it has been applied to the characterization of various dynamical phenomena, such as the diffusion of innovation [ 30 ] or recurring fashion cycles [ 31 ]. It is also worth mentioning that, when considered in duplex and multiplex settings, the q -voter model provides a very rich behaviour with respect to the observed phase transitions [ 32 , 33 ]. Considering these observations, we eventually select the q -voter model due to its apparent simplicity and low number of tunable parameters that can lead to complex results.…”

Section: Introductionmentioning

confidence: 99%

Role of Time Scales in the Coupled Epidemic-Opinion Dynamics on Multiplex Networks

Jankowski

Chmiel

2022

Entropy

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Modelling the epidemic’s spread on multiplex networks, considering complex human behaviours, has recently gained the attention of many scientists. In this work, we study the interplay between epidemic spreading and opinion dynamics on multiplex networks. An agent in the epidemic layer could remain in one of five distinct states, resulting in the SIRQD model. The agent’s attitude towards respecting the restrictions of the pandemic plays a crucial role in its prevalence. In our model, the agent’s point of view could be altered by either conformism mechanism, social pressure, or independent actions. As the underlying opinion model, we leverage the q-voter model. The entire system constitutes a coupled opinion–dynamic model where two distinct processes occur. The question arises of how to properly align these dynamics, i.e., whether they should possess equal or disparate timescales. This paper highlights the impact of different timescales of opinion dynamics on epidemic spreading, focusing on the time and the infection’s peak.

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“…Both the existence and the distinction between different types of phase transitions seems to be in the field of big interest of many researchers. This topic was not only reviewed from theoretical point of view in dynamical like models [1][2][3] but it appears in real social systems [4][5][6][7][8]. Through the need to establish certain universal laws, scientists are looking for factors which influence the appearance of discontinuous phase transitions.…”

Section: Introductionmentioning

confidence: 99%

Switching from a continuous to discontinuous phase transition under the quenched disorder

Nowak,

Sznajd-Weron

2021

Preprint

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We study the generalized version of the q-voter model with anticonformity in which agents can be in one of s 2 states. As in the original model, which corresponds to s = 2, unanimous group of q agents can influence the choosen voter (conformity) or he can take one of values diffrent than value of them (anticonformity). In our generalization we consider two types of disorder: (1) annealed, where voter act as anticonformist with probability p and with complementary probability 1 − p conform to others, and (2) quenched, where a fraction p of all voters are permanently anticonformists and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo sumulations. We show, in contrast to common knowledge, that the model with quenched randommness can express discontinuous phase transitions for q > 1, whereas annealed scheme displays only continous phase transitions.

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A Veritable Zoology of Successive Phase Transitions in the Asymmetric q-Voter Model on Multiplex Networks

Cited by 19 publications

References 40 publications

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

Role of Time Scales in the Coupled Epidemic-Opinion Dynamics on Multiplex Networks

Switching from a continuous to discontinuous phase transition under the quenched disorder

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