This was part of Mean-Field Models for Interacting Agents

Aggregation without Attraction

Angelika Manhart, University College London

Thursday, November 4, 2021


Aggregation of individuals, such as people, bacteria or sperm, is an ubiquitous phenomenon and is often attributed to direct attraction between the agents. In this talk I will present a basic model that suggests how aggregation can also be a consequence of interactions with an elastic environment.

I will start with a stochastic individual-based model (IBM) of collectively moving self-propelled swimmers and elastically tethered obstacles. Simulations reveal at least three distinct large-scale patterns: travelling bands, trails and moving clusters. This motivates the derivation of a macroscopic partial differential equations (PDE) model for swimmer-obstacle interactions, for which we assume strong obstacle springs. The result is a coupled system of non-linear, non-local PDEs. Linear stability analysis allows to investigate pattern appearance and properties. Close inspection of the derived convolution operator in the PDE model reveals short-ranged swimmer aggregation, irrespective of whether obstacles and swimmers are attractive or repulsive.