We develop a agent-based framework to model the emergence of collective
emotions, which is applied to online communities. Agents individual emotions
are described by their valence and arousal. Using the concept of Brownian
agents, these variables change according to a stochastic dynamics, which also
considers the feedback from online communication. Agents generate emotional
information, which is stored and distributed in a field modeling the online
medium. This field affects the emotional states of agents in a non-linear
manner. We derive conditions for the emergence of collective emotions,
observable in a bimodal valence distribution. Dependent on a saturated or a
superlinear feedback between the information field and the agent's arousal, we
further identify scenarios where collective emotions only appear once or in a
repeated manner. The analytical results are illustrated by agent-based computer
simulations. Our framework provides testable hypotheses about the emergence of
collective emotions, which can be verified by data from online communities.Comment: European Physical Journal B (in press), version 2 with extended
introduction, clarification