Phase change in an opinion-dynamics model with separation of time scales

We define an opinion formation model of agents in a one-dimensional ring, where the opinion of an agent evolves due to its interactions with close neighbors and due to its either positive or negative attitude toward the overall mood of all the other agents. While the dynamics of the agent's opinion is described with an appropriate differential equation, from time to time pairs of agents are allowed to change their locations to improve the homogeneity of opinion (or comfort feeling) with respect to their short-range environment. In this way the timescale of transaction dynamics and that of environment update are well separated and controlled by a single parameter. By varying this parameter we discovered a phase change in the number of undecided individuals. This phenomenon arises from the fact that too frequent location exchanges among agents result in frustration in their opinion formation. Our mean field analysis supports this picture.