TY - JOUR

T1 - From Continuous to Discontinuous Transitions in Social Diffusion

AU - Tuzón, Paula

AU - Fernández-Gracia, Juan

AU - Eguíluz, Víctor M.

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: JF-G and VE received funding from Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) through project SPASIMM [FIS2016-80067-P (AEI/FEDER, UE)]. Research reported in this publication was supported by research funding from King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2018/3/7

Y1 - 2018/3/7

N2 - Models of social diffusion reflect processes of how new products, ideas, or behaviors are adopted in a population. These models typically lead to a continuous or a discontinuous phase transition of the number of adopters as a function of a control parameter. We explore a simple model of social adoption where the agents can be in two states, either adopters or non-adopters, and can switch between these two states interacting with other agents through a network. The probability of an agent to switch from non-adopter to adopter depends on the number of adopters in her network neighborhood, the adoption threshold T and the adoption coefficient a, two parameters defining a Hill function. In contrast, the transition from adopter to non-adopter is spontaneous at a certain rate μ. In a mean-field approach, we derive the governing ordinary differential equations and show that the nature of the transition between the global non-adoption and global adoption regimes depends mostly on the balance between the probability to adopt with one and two adopters. The transition changes from continuous, via a transcritical bifurcation, to discontinuous, via a combination of a saddle-node and a transcritical bifurcation, through a supercritical pitchfork bifurcation. We characterize the full parameter space. Finally, we compare our analytical results with Monte Carlo simulations on annealed and quenched degree regular networks, showing a better agreement for the annealed case. Our results show how a simple model is able to capture two seemingly very different types of transitions, i.e., continuous and discontinuous and thus unifies underlying dynamics for different systems. Furthermore, the form of the adoption probability used here is based on empirical measurements.

AB - Models of social diffusion reflect processes of how new products, ideas, or behaviors are adopted in a population. These models typically lead to a continuous or a discontinuous phase transition of the number of adopters as a function of a control parameter. We explore a simple model of social adoption where the agents can be in two states, either adopters or non-adopters, and can switch between these two states interacting with other agents through a network. The probability of an agent to switch from non-adopter to adopter depends on the number of adopters in her network neighborhood, the adoption threshold T and the adoption coefficient a, two parameters defining a Hill function. In contrast, the transition from adopter to non-adopter is spontaneous at a certain rate μ. In a mean-field approach, we derive the governing ordinary differential equations and show that the nature of the transition between the global non-adoption and global adoption regimes depends mostly on the balance between the probability to adopt with one and two adopters. The transition changes from continuous, via a transcritical bifurcation, to discontinuous, via a combination of a saddle-node and a transcritical bifurcation, through a supercritical pitchfork bifurcation. We characterize the full parameter space. Finally, we compare our analytical results with Monte Carlo simulations on annealed and quenched degree regular networks, showing a better agreement for the annealed case. Our results show how a simple model is able to capture two seemingly very different types of transitions, i.e., continuous and discontinuous and thus unifies underlying dynamics for different systems. Furthermore, the form of the adoption probability used here is based on empirical measurements.

UR - http://hdl.handle.net/10754/629758

UR - http://journal.frontiersin.org/article/10.3389/fphy.2018.00021/full

UR - http://www.scopus.com/inward/record.url?scp=85043781934&partnerID=8YFLogxK

U2 - 10.3389/fphy.2018.00021

DO - 10.3389/fphy.2018.00021

M3 - Article

VL - 6

JO - Frontiers in Physics

JF - Frontiers in Physics

SN - 2296-424X

IS - MAR

ER -