Mathematical analysis on the collective behaviors of agent-based model

Abstract

In this thesis, we study collective behaviors of agent-based model. In Chapter 2, we present preliminary properties of Cucker-Smale type model and Kuramoto type model. In Chapter 3, we prove a generalized ocking estimate for the Cucker-Smale type model. In Chapter 4, we study about global existence for the Cucker-Smale type model with singular weights and the Cucker-Smale model with a bonding force. In Chapter 5, we study about the Kuramoto type model with the nearest neighbor interactions in a ring. Finally, in Chapter 6, we conclude this thesis with mathematical problems related by agent-based model.