Flocks with Nonlinear Inherent Dynamics under Fixed and Switching Digraphs

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 2, Page 1242-1271, June 2024.
Abstract.This paper studies the dynamic interplay between inherent agent dynamics and velocity alignment in the ensemble of Cucker–Smale (CS) flocks under both fixed and switching interaction topologies. For the fixed topology network modeled by a rooted digraph, we provide sufficient frameworks for exponential convergence of flocking provided that the Lipschitz constant of nonlinear dynamics is less than a given bound in terms of initial state and system parameters. Similar to the CS system free of inherent dynamics, our results exhibit threshold phenomena depending on the quantity of collectivity in of the rooted digraph. For the case with switching topologies being rooted in a sequence of time-blocks, we present similar sufficient frameworks leading to convergence of flocking in terms of initial state and system parameters. Our results hold for both continuous time and discrete time. Numerical simulations are performed to illustrate our theoretical results.