Flexible evolution of flocking tracking for a nonlinear collective migration model with heterogeneous transmission delays

Division of labour and cooperation in animal groups is an external manifestation of swarm intelligence, such as leaders and followers in collective migration of animals. In this paper, we propose a nonlinear multi-agent system named collective migration model and try to build a more realistic dynamic leader–follower structure that facilitates flexible evolution of flocking tracking. The model highlights individual heterogeneity, especially including heterogeneous transmission delays among agents and heterogeneous parameters called tracking strategies that establish a trade-off between alignment and tracking for each agent, and essentially determine the leader–follower structure of the system. By constructing dynamic upper bounds of velocity, setting tracking periods and partitioning state space, a time-varying tracking strategy vector is designed to produce a dynamic leader–follower structure in which the system has a flexible configuration and can achieve flocking tracking for any initial state. The increase of transmission delay prolongs the switching cycle of leader–follower structure, and decreases the convergence speed of the system. An algorithm of the tracking strategy vector and several numerical simulations are provided to verify our results.