2025/12/25 by Li, Hsin-Lun
#05C82 #60G42 #93D20 #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 93D50 #Secondary 93C10 #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2512.21721
We study a discrete-time consensus model in which agents iteratively update their states through interactions on a dynamic social network. At each step, a single agent is selected asynchronously and averages the values of its current neighbors. A distinctive feature of our model is that an agent's neighborhood may contract following an update, while non-selected agents may add or remove neighbors independently. This creates a time-varying communication structure with endogenous contraction. We show that under mild assumptions--specifically, that the evolving graph is connected infinitely often--the system reaches consensus almost surely. Our results extend classical consensus theory on time-varying graphs and asynchronous updates by introducing selective neighborhood contraction, offering new insights into agreement dynamics in evolving social systems.