Fast-Slow Reduction and Bifurcation Dynamics of a Spatial Intraguild Predation Model with Resource Refuge: Deterministic and Stochastic Robustness Analysis

Research Question

How do spatial refuge, fast resource migration, and environmental noise affect coexistence, oscillations, and collapse in an intraguild predation system?

Abstract

Intraguild predation (IGP) systems capture essential ecological interactions where species both compete and prey upon each other while sharing a common resource. Understanding how spatial structure and environmental variability jointly influence these dynamics remains a key challenge in ecological modelling. In this study, we analyse an IGP system in a heterogeneous two-patch environment, where the basal resource undergoes rapid migration between a refuge and a predation patch. Using time-scale separation and aggregation-of-variables techniques, we derive a reduced-order model that governs the slow dynamics of total resource biomass and predator populations. The reduced model enables efficient simulation and analytical investigation of the system. A detailed bifurcation analysis reveals a rich set of dynamical regimes, including stable coexistence, oscillatory behaviour induced by Hopf bifurcations and trophic collapse. To assess the robustness of these dynamics, we extend the model to incorporate environmental stochasticity affecting key parameters such as growth rates and predation efficiencies. Numerical simulations show that while the main bifurcation structure persists under moderate noise, stochastic perturbations can induce regime shifts, amplify oscillations, and accelerate extinction events near critical thresholds. These findings demonstrate that reduced-order modelling combined with stochastic simulation provides a powerful framework for analysing complex ecological systems under uncertainty. The results highlight the dual role of spatial structure and environmental variability in shaping ecosystem stability and resilience

What This Paper Does

The paper reduces a two-patch ecological model using time-scale separation, analyzes equilibria and bifurcations, and tests the robustness of the resulting dynamics under environmental stochasticity.

My Contribution

• Analyzed equilibrium points and their stability in the proposed dynamical system and conducted theoretical analysis of the stochastic PDE model under Brownian perturbations.
• Implemented Maple simulations to validate analytical results and generate numerical figures and drafted paper.