Tuesday, January 22, 2013

1301.4751 (Huiseung Chae et al.)

Phase transitions in Paradigm models    [PDF]

Huiseung Chae, Soon-Hyung Yook, Yup Kim
In this letter we propose two general models for paradigm shift, deterministic propagation model (DM) and stochastic propagation model (SM). By defining the order parameter $m$ based on the diversity of ideas, $\Delta$, we study when and how the transition occurs as a cost $C$ in DM or an innovation probability $\alpha$ in SM increases. In addition, we also investigate how the propagation processes affect on the transition nature. From the analytical calculations and numerical simulations $m$ is shown to satisfy the scaling relation $m=1-f(C/N)$ for DM with the number of agents $N$. In contrast, $m$ in SM scales as $m=1-f(\alpha^a N)$.
View original: http://arxiv.org/abs/1301.4751

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