Collective Dynamics in Biological and Social Systems

Nonlocal interaction equations: phenomena and structures

Dejan Slepcev

Carnegie Mellon University

Nonlocal-interaction equations serve as one of the basic models of biological aggregation. The interaction between individuals is typically attractive at large distances and repulsive at short distances. We will discuss several phenomena appearing in systems governed by such interactions and mathematical structures used to describe them. In particular the variety of patterns that stable steady states exhibit, rolling swarms in heterogeneous environments, and systems where the long-range interaction is attenuated by the crowdedness.