Barrier-mediated predator-prey dynamics

Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf 40225 Düsseldorf, Germany

^(a) Fabian.Schwarzendahl@hhu.de (corresponding author)

Received: 22 March 2021
Accepted: 27 May 2021

Abstract

The survival chance of a prey chased by a predator depends not only on their relative speeds but importantly also on the local environment they have to face. Here, we propose a simple predator-prey model for a situation in which both the escaping prey and the chasing predator have to surmount an energetic barrier. Different barrier-assisted states of catching or final escaping are classified and suitable scaling laws separating these two states are derived. We discuss the effect of fluctuations on the catching times and determine states in which catching or escaping is more likely. We further identify trapping or escaping states which are determined by hydrodynamics and chemotactic interactions. Our results are of importance for both microbes and self-propelled unanimate microparticles following each other by non-reciprocal interactions in inhomogeneous landscapes.