Two-Population Social Cycle Theories

Callahan, Gene; Hoffmann, Andreas

doi:10.2139/ssrn.2560270

Cited by 2 publications

(2 citation statements)

References 8 publications

(3 reference statements)

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“…We therefore have a mechanism for the endogenous generation of periodic fads and fashions. We note that a quite different mechanism capable of generating periodic fashions, based on 'snobs' and 'followers', is modelled in [1,5]. We note that endogenous oscillations do not occur in the basic models of mathematical epidemiology, and some special mechanisms are required to generate such oscillations, the most prominent being temporary immunity with delay [25,49].…”

Section: Discussionmentioning

confidence: 99%

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The dynamics of two-stage contagion

Katriel

2019

Chaos, Solitons & Fractals: X

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We explore simple models aimed at the study of social contagion, in which contagion proceeds through two stages. When coupled with demographic turnover, we show that two-stage contagion leads to nonlinear phenomena which are not present in the basic 'classical' models of mathematical epidemiology. These include: bistability, critical transitions, endogenous oscillations, and excitability, suggesting that contagion models with stages could account for some aspects of the complex dynamics encountered in social life. These phenomena, and the bifurcations involved, are studied by a combination of analytical and numerical means.

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Section: Discussionmentioning

confidence: 99%

“…the contagion-free equilibrium E 0 is stable, but there exist also two endemic equilibria E 1 , E 2 , with E 1 stable and E 2 unstable (propositions 3,5,6). Thus in this region we have bistability -the contagion may persist or not, depending on the initial conditions.…”

Section: Region Ii: Bistabilitymentioning

confidence: 97%

The dynamics of two-stage contagion

Katriel

2019

Chaos, Solitons & Fractals: X

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The Hunt Opinion Model—An Agent Based Approach to Recurring Fashion Cycles

et al. 2016

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We study a simple agent-based model of the recurring fashion cycles in the society that consists of two interacting communities: “snobs” and “followers” (or “opinion hunters”, hence the name of the model). Followers conform to all other individuals, whereas snobs conform only to their own group and anticonform to the other. The model allows to examine the role of the social structure, i.e. the influence of the number of inter-links between the two communities, as well as the role of the stability of links. The latter is accomplished by considering two versions of the same model—quenched (parameterized by fraction L of fixed inter-links) and annealed (parameterized by probability p that a given inter-link exists). Using Monte Carlo simulations and analytical treatment (the latter only for the annealed model), we show that there is a critical fraction of inter-links, above which recurring cycles occur. For p ≤ 0.5 we derive a relation between parameters L and p that allows to compare both models and show that the critical value of inter-connections, p*, is the same for both versions of the model (annealed and quenched) but the period of a fashion cycle is shorter for the quenched model. Near the critical point, the cycles are irregular and a change of fashion is difficult to predict. For the annealed model we also provide a deeper theoretical analysis. We conjecture on topological grounds that the so-called saddle node heteroclinic bifurcation appears at p*. For p ≥ 0.5 we show analytically the existence of the second critical value of p, for which the system undergoes Hopf’s bifurcation.

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Two-Population Social Cycle Theories

Cited by 2 publications

References 8 publications

The dynamics of two-stage contagion

The dynamics of two-stage contagion

The Hunt Opinion Model—An Agent Based Approach to Recurring Fashion Cycles

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