  We investigate the collective motion of self-propelled agents in an
environment filled with obstacles that are tethered to fixed positions via
springs. The active particles are able to modify the environment by moving the
obstacles through repulsion forces. This creates feedback interactions between
the particles and the obstacles from which a breadth of patterns emerges
(trails, band, clusters, honey-comb structures,...). We will focus on a
discrete model first introduced in [Aceves2020] and derived into a continuum
PDE model. As a first major novelty, we perform an in-depth investigation of
pattern formation of the discrete and continuum models in 2D: we provide
phase-diagrams and determine the key mechanisms for bifurcations to happen
using linear stability analysis. As a result, we discover that the agent-agent
repulsion, the agent-obstacle repulsion and the obstacle's spring stiffness are
the key forces in the appearance of patterns, while alignment forces between
the particles play a secondary role. The second major novelty lies in the
development of an innovative methodology to compare discrete and continuum
models that we apply here to perform an in-depth analysis of the agreement
between the discrete and continuum models.
