Prey Refugia as a Mechanism for Ecological Resilience: A Mathematical and Numerical Analysis Through Isospike Diagrams

Prey refuge is widely recognized as a critical ecological mechanism that shapes species persistence and ecosystem stability. While most existing studies have focused on lower-dimensional predator–prey models, the stabilizing and destabilizing roles of refuge in higher-dimensional trophic structures remain underexplored. In this study, we investigate the dynamics of a four-dimensional diamond-shaped food web in which refuge is incorporated at the basal prey level. Using isospike diagrams as a novel diagnostic tool, we uncover a spectrum of complex dynamical behaviors, including shrimp-shaped periodic windows, period bubbling, coexistence of multiple attractors, and predator extinction scenarios. These periodic windows form well-structured islands embedded within chaotic regimes, demonstrating that small parameter changes can recover stability from apparent randomness. Our results reveal that moderate refuge levels suppress chaos and promote equilibrium, whereas excessive refuge induces oscillations or top predator extinction, underscoring the double-edged ecological role of this mechanism. These findings extend the classical stabilizing interpretation of prey refuge to higher-dimensional systems and highlight its potential to either buffer or destabilize ecological networks depending on intensity. By integrating nonlinear dynamical analysis with ecological interpretation, our work provides new insights into the resilience and fragility of complex food webs and establishes isospike diagrams as a powerful tool for exploring higher-dimensional ecological models. Overall, the study highlights the dual role of prey refuges: in most cases stabilizing multitrophic dynamics, but occasionally acting as a source of instability in complex ecological networks.