Partially satisfied to fully satisfied transitions in co-evolving inverse voter model and possible scaling behavior

• Identified key features and phase transitions in coevolving inverse voter model.
• Constructed a better theory incorporating longer spatial correlation.
• Proposed scaling variable and illustrated possible scaling behavior.
• Used scaling behavior to predict results of IVM in a different network.

Understanding co-evolving networks characterized by the mutual influence of agents' actions and network structure remains a challenge. We study a co-evolving inverse voter model in which agents adapt to achieve a preferred environment with more opposite-opinion neighbors by rewiring their connections and switching opinion. Numerical studies reveal a transition from a dynamic partially satisfied phase to a frozen fully satisfied phase as the rewiring probability is varied. A simple mean field theory is shown to capture the behavior only qualitatively. An improved mean field theory carrying a longer spatial correlation gives better results. Motivated by numerical results in networks of different degrees and mean field results, we propose a scaling variable that combines the rewiring probability and mean degree in a special form. The scaling variable is shown to work well in analyzing data corresponding to different networks and different rewiring probabilities. An application is to predict the results for networks of different degrees based solely on results obtained from networks of one degree. Studying scaling behavior provides an alternative path for understanding co-evolving agent-based dynamical systems, especially in light of the trade-off between complexity of a theory and its accuracy.