Adaptive Cucker-Smale Model and its Asymptotic Behavior in the Singular Limit
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In this talk, we introduce an adaptive network within Cucker-Smale (CS) dynamics. The properties of adaptive network allow particles in the CS regime to form and break up groups of neighbors, resulting in the emergence of diverse patterns. We investigate the singular limit of the adaptive CS model to better understand the role of the adaptive rule, which transforms the system into Laplacian dynamics on a temporal graph. Through the analysis of Laplacian dynamics on various types of temporal graphs, we demonstrate the asymptotic behavior of the adaptive CS model in this singular limit.