2021/02/07 by Guy A Djokam, Djokam, Guy A, Muruhan Rathinam +1
Mathematics · #92-10 #93A16 #93C70 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:92-10 #msc:93A16 #msc:93C70
paper · pdf · doi:10.48550/arxiv.2102.03862
28 pages, 8 figures
arxiv created 2022/02/20 · arxiv updated 2022/02/22
We introduce and analyze a model for the dynamics of flocking and steering of a finite number of agents. In this model, each agent's acceleration consists of flocking and steering components. The flocking component is a generalization of many of the existing models and allows for the incorporation of many real world features such as acceleration bounds, partial masking effects and orientation bias. The steering component is also integral to capture real world phenomena. We provide rigorous sufficient conditions under which the agents flock and steer together. We also provide a formal singular perturbation study of the situation where flocking happens much faster than steering. We end our work by providing some numerical simulations to illustrate our theoretical results.