Kuramoto Model of Weakly Conformed Oscillators

Conformity is a common phenomenon which is observed in social psychology, group decision making, and animal behavior. Inspired by the experiments of Moiseff and Copeland, in which they found that the response of female Photinus carolinus to computer flashes depends grossly on the synchrony of flashes, we consider a Kuramoto model with weakly conformed oscillators to study the effects of conformity on synchronization. In our model, the tendency of individual oscillator catching up each other varies with the degree of synchronization that mimics the conformity effect. While considering unimodal frequency distribution, a hysteresis loop emerges in the bifurcation diagram and the branch of unstable fixed points corresponds to the threshold, or "quorum", over which systems move toward more synchronized states. This result is similar to quorum response of consensus decision making, which a consensus decision is finally reached by entire group (oscillators reach synchronized states) once the population supporting it exceeds a quorum (once the degree of synchronization exceeds the threshold)