Discrete Infinite‐Agent Cucker–Smale Flocking Under Fixed and Switching Digraphs

ABSTRACT This paper studies the flocking behavior in a discrete‐time Cucker–Smale (C‐S) model with infinite agents under both fixed and switching directed interaction topologies. For the fixed topology, we analyze the infinite digraph containing a spanning tree with the finite smallest depth under two distinct framework conditions. We then show that unconditional and conditional flocking can occur, consistent with the behavioral patterns of finite‐dimensional C‐S systems under fixed digraphs. For the switching topologies, we derive analogous sufficient conditions that guarantee the occurrence of flocking. The theoretical results are further illustrated through several examples.