Interplay of the unit-speed constraint and time-delay in Cucker-Smale flocking

We study the emergence of the mono-cluster flocking due to the interplay between the unit-speed constraint and time-delayed interactions in the evolution of the Cucker-Smale ensemble. Several flocking models with unit-speed constraint have been extensively used in the flocking modeling of self-propelled multi-agent systems in the control theory community. Time-delayed interactions can be caused by the finite propagation speed constraint in communications. In the previous literature, these two physical mechanisms have been studied separately. In this paper, we investigate these combined physical effects in a common framework and study how the interplay between these mechanisms affects asymptotic flocking dynamics. For this, we provide a sufficient framework for a mono-cluster flocking in terms of system parameters (e.g., time-delay, coupling strength, particle numbers) and initial data. We also provide several numerical simulations and compare them with analytical results.