SFU Mathematics of Computation, Application and Data ("MOCAD") Seminar: Hansol Park

In this talk, I introduce several first- and second-order models for self-collective behaviour on general manifolds and discuss their emergent behaviors. For the first-order model, we consider attractive-repulsive and purely attractive interaction potentials, and investigate the equilibria and the asymptotic behaviour of the solutions. In particular, we quantify the approach to asymptotic consensus in terms of the convergence rate of the diameter of the solution’s support. For the second-order model (known as the Cucker-Smale model), velocity alignment interactions are considered. To analyze the emergent behaviors of the two models, the LaSalle invariance principle is used. Also, various geometric tools used to analyze the aggregation models on manifolds are presented.