Flocking of Multi-Particle Swarm with Group Coupling Structure and Measurement Delay (Journal of Nonlinear Modeling and Analysis, 2024)
We investigate the flocking conditions of a group coupling system with time delays, in which the communication between particles includesinter-group and intra-group interactions, and the time delay comes from thetheory of moving object observation. As an effective model, we introduce asystem of nonlinear functional differential equations to describe its dynamicevolution mechanism. By constructing two differential inequalities on velocityand velocity fluctuation from a continuity argument, and using the Lyapunovfunctional approach, we present some sufficient conditions for the existenceof asymptotic flocking solutions to the coupling system, in which an upperbound of the delay allowed by the system is quantitatively given to ensure theemergence of flocking behavior. All results are novel and can be illustrated byusing some specific numerical simulations.
Keywords: Time-asymptotic flocking; Group coupling; Intra-group and inter-group interaction; Measurement delay.