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.