Complex dynamics in prey-predator systems with cross-coupling: Exploring nonlinear interactions and population oscillations

This study investigates the problem of ecosystem dynamics in fragmented landscapes, specifically focusing on a two-patch environment with interacting prey and predators. The research examines the impact of cross-predation on these interactions. Using bifurcation analysis, we explored the structural arrangement of attractors and identified complex dynamics such as symmetric, asymmetric, and asynchronous attractors induced by varying cross-coupling levels. Notably, our study describes a novel mechanism for the formation of anti-phase synchrony in the patches. Unlike typical occurrences of a cycle following Hopf bifurcation, our model reveals that the anti-phase cycle stabilizes via Neimark-Sacker (NS) bifurcation of a two- period unstable cycle branch emanating from the synchronous cycle branch. Our findings also demonstrate that cross-feeding can lead to significant ecosystem asymmetry and branching, culminating in the dominance of a single cross-feeding chain. These results challenge traditional models and highlight the presence of multistability and the potential for ecosystem evolution towards distinct subsystem branches due to cross-predation. The study's insights offer valuable contributions to population and evolutionary biology, enhancing our understanding of the intricate dynamics within fragmented ecosystems.