Emergence of state-locking for the first-order nonlinear consensus model on the real line

We propose a general nonlinear consensus model and study its asymptotic behaviors. The proposed consensus model is motivated by the one-dimensional relativistic Cucker-Smale (RCS) model which corresponds to the relativistic counterpart of the Cucker-Smale (CS) flocking model. Depending on the regularity and singularity of communication weight at the origin and far-field, we provide diverse clustering patterns for the collective behaviors of the proposed model. We also study the structural stability of the proposed model with respect to coupling function.