Convergence Analysis of Classes of Asymmetric Networks of Cucker-Smale Type with Deterministic Perturbations

We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence of identical internal dynamics. The second model describes a similar population of agents that perform velocity alignment with the restriction of collision-free orbits. Although qualitatively different, we explain how these two non-trivial types of perturbations are analyzed under a unified framework. Rigorous analysis is conducted towards establishing new sufficient conditions for asymptotic flocking to a synchronized motion. Applications of our results are compared with simulations to illustrate the effectiveness of our theoretical estimates.