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.

中文翻译：

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具有交叉耦合的猎物-捕食者系统中的复杂动力学：探索非线性相互作用和种群振荡


这项研究调查了破碎景观中的生态系统动态问题，特别关注猎物和捕食者相互作用的两块环境。该研究探讨了交叉捕食对这些相互作用的影响。使用分叉分析，我们探索了吸引子的结构排列，并识别了复杂的动力学，例如由不同交叉耦合水平引起的对称、不对称和异步吸引子。值得注意的是，我们的研究描述了一种在贴片中形成反相同步的新机制。与 Hopf 分岔后周期的典型出现不同，我们的模型揭示了反相周期通过源自同步周期分支的两周期不稳定周期分支的 Neimark-Sacker (NS) 分叉而稳定。我们的研究结果还表明，交叉喂养可能导致严重的生态系统不对称和分支，最终导致单一交叉喂养链的主导地位。这些结果挑战了传统模型，并强调了多稳定性的存在以及由于交叉捕食而导致生态系统向不同子系统分支进化的潜力。该研究的见解为种群和进化生物学做出了宝贵的贡献，增强了我们对支离破碎的生态系统内复杂动态的理解。