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

TL;DR

This paper analyzes two nonlinear perturbed asymmetric Cucker-Smale models, establishing new conditions for flocking and synchronization, supported by simulations demonstrating the theoretical results' effectiveness.

Contribution

It introduces a unified framework for analyzing two types of nonlinear perturbations in asymmetric Cucker-Smale models, deriving new flocking conditions.

Findings

Established sufficient conditions for asymptotic flocking.

Unified analysis framework for different perturbation types.

Validated theoretical results with simulations.

Abstract

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.