标题： 水分渗透-土壤湿度反馈的动态耦合：水-植被模型中的涌现植被模式 显示英文标题

标题： Dynamic Coupling of Infiltration-Soil Moisture Feedback:Emergent Vegetation Patterns in a Water-Vegetation Model

摘要： 我们提出了一种改进的水-植被模型，以研究渗透-土壤湿度反馈与干旱/半干旱生态系统中植被模式之间的机制关系。 利用图灵模式形成理论，我们推导了扩散诱导不稳定的条件，并分析了图灵-霍普夫分岔点附近的时空动力学。 我们的主要发现包括：(i) 该系统表现出丰富的动态特性，包括多个稳定平衡点、超临界/亚临界霍普夫分岔、极限环的气泡环和同宿分岔。 (ii) 该系统存在图灵-霍普夫分岔。 使用规范型理论，我们在临界阈值附近建立了准周期解和混合模式振荡的存在性，为预测非线性生态制度转变提供了数学框架。 (iii) 土壤湿度反馈控制三种不同生态系统状态之间的关键转变：均匀植被覆盖状态、自组织空间模式（迷宫状/有间隙的植被）和裸土状态，这表明土壤湿度阈值控制该系统最终状态的选择。 显示英文摘要

摘要： We present a modified water-vegetation model to investigate the mechanistic relationship between infiltration-soil moisture feedback and vegetation pattern in arid/semi-arid ecosystems. Employing Turing pattern formation theory, we drive conditions for diffusion-induced instability and analyze spatiotemporal dynamics near Turing-Hopf bifurcation points. Our key findings include: (i) The system exhibits rich dynamics including multiple stable equilibria, supercritical/subcritical Hopf bifurcations, bubble loops of limit cycles and homoclinic bifurcations. (ii) The system admits Turing-Hopf bifurcation. Using normal form theory, we establish the existence of quasiperiodic solutions and mixedmode oscillations near critical thresholds, providing a mathematical framework for predicting nonlinear ecological regime shifts. (iii) Soil moisture feedbacks govern critical transitions between three distinct ecosystem states: uniform vegetation covering, self-organized spatial patterns (labyrinth/gapped vegetation), and bare soil state, which demonstrates that soil moisture thresholds control the final state selection in this system.