Beijing Institute of Mathematical Sciences and Applications

This course systematically explores the fundamental principles, mathematical models, and applications of swarm dynamics in both natural and artificial systems. Beginning with collective behaviors in biological groups (such as bird flocks, fish schools, and insect cooperation), the course reveals the dynamical principles behind self-organization and emergent phenomena, extending to human communities, robot swarms, traffic flow, and distributed artificial intelligence.
Through theoretical instruction, numerical simulation, and case studies, students will master core theoretical frameworks of collective behavior (such as the Vicsek model, Boids algorithm, and individual-based modeling approaches), learn how simple rules can drive complex global behaviors, and understand the impact of network topology, noise, and interaction range on system stability. The course will also incorporate cutting-edge research to explore practical applications of swarm dynamics in drone formation control, intelligent traffic optimization, social network analysis, and ecosystem management.