Emergent Dynamics of an Orientation Flocking Model With Distance‐Dependent Delay

ABSTRACT In this paper, we investigate the dynamical behaviors of an orientation flocking model that incorporates state‐dependent delay. The research unfolds in three principal phases: First, we establish the global existence and uniqueness of solutions for our system. Subsequently, we develop a comprehensive theoretical framework that provides sufficient conditions for the emergence of orientation flocking phenomena. In particular, this framework remains valid regardless of the number of particles . In the final phase of our analysis, we perform a systematic derivation of the mean‐field limit for the discrete system, accompanied by a proof of global well‐posedness for the resulting mean‐field equations. Furthermore, we demonstrate that our theoretical results and analytical framework naturally extend to and encompass the case of orientation flocking models with constant time delays.