Phase transitions in paradigm shift models.
Two general models for paradigm shifts, deterministic propagation model (DM) and stochastic propagation model (SM), are proposed to describe paradigm shifts and the adoption of new technological levels. By defining the order parameter m based on the diversity of ideas, Δ, it is studied when and how the phase transition or the disappearance of a dominant paradigm occurs as a cost C in DM or an innovation probability α in SM increases. In addition, we also investigate how the propagation processes affect the transition nature. From 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(α(a)N).
Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul, Korea.
Huiseung
H
Chae
Soon-Hyung
SH
Yook
Yup
Y
Kim
D003198:Computer Simulation; D008956:Models, Chemical; D044367:Phase Transition; D011336:Probability; D013269:Stochastic Processes