Collective Behavior Modeling Through Velocity Alignment

Abstract

We construct a model for collective behavior phenomena by undermining the assumption that the rate of change of position equals velocity in the particle Cucker-Smale model for flocking. Conditions for collective behavior are proven and three continuous models for segregation are presented with simulations for two of them. Future avenues of research and a variety of applications such as social science, engineering, and business trends are discussed in the conclusion.