Speaker:  Yicheng Liu  （刘易成）
Title: Consensus behaviors analysis for delayed opinion systems

Time: 2015年03月15日10：00-11：00

Location: Center for Mathematical Sciences, Room 813

Abstract：In this talk, we consider the case when zero is a semi-simple eigenvalue of the normalized connection matrix, and we expand the concept of consensus where opinions of all individual agents must converge to the common (consensus) value to the weak consensus where opinions are clustered and the consensus value is no longer a scalar constant but a vector in a certain consensus subspace. The linearity of the system enables us to adopt an argument of Atay, using the phase space decomposition in terms of the standard bilinear form for functional differential equations, to derive sharp conditions for the system to reach a weak consensus, and to calculate the consensus vector. This calculation also informs how the consensus value of the coupled systems depends on the consensus of the subgroups, initial conditions and communication delay. Also, the flocking patterns are present at last section.  This is a joint work with Jianhong Wu.