Bifurcation analysis of an agent-based model for predator–prey interactions

• We study an agent-based and an aggregate model for predator–prey interactions.
• The two models share coexistence, collapse and oscillatory behaviour.
• They exhibit similar bifurcation sequences.
• Advanced spectral methods reliably detect Hopf bifurcation in the agent-based model.
• Slowdown in recovery anticipates a global bifurcation.

The Rosenzweig–MacArthur model is a set of ordinary differential equations (ODEs) that provides an aggregate description of the dynamics of a predator–prey system. When including an Allee effect on the prey, this model exhibits bistability and contains a pitchfork bifurcation, a Hopf bifurcation and a heteroclinic bifurcation. We develop an agent-based model (ABM) on a two-dimensional, square lattice that encompasses the key assumptions of the aggregate model. Although the two modelling approaches – ODE and ABM – differ, both models exhibit similar bifurcation patterns. The ABM model's behaviour is richer and it is analysed using advanced statistical methods. In particular, singular spectrum analysis is used to robustly locate the transition between apparently random, small-amplitude fluctuations around a fixed point and stable, large-amplitude oscillations. Critical slowing down of model trajectories anticipates the heteroclinic bifurcation. Systematic comparison between the ABM and the ODE models’ behaviour helps one understand the predator–prey system better; it provides guidance in model exploration and allows one to draw more robust conclusions on the nature of predator–prey interactions.