[论文解读] How inertia affects autotoxicity-mediated vegetation dynamics: from close-to to far-from-equilibrium patterns

Giancarlo Consolo, Carmela Currò+4 more|arXiv (Cornell University)|Mar 10, 2026

Ecosystem dynamics and resilience被引用 0

一句话总结

本文在 Klausmeier 模型中加入惯性和自毒性，用以研究坡度干旱地区的植被格局，详细分析惯性如何通过分析与数值方法影响起始、波不稳定性、行进脉冲和迟滞。

ABSTRACT

In this work, the influence of inertial effects on the formation and evolution of vegetation patterns on sloped arid terrains is investigated from the onset of instability to far-from-equilibrium. Analyses are carried out in a hyperbolic extension of the one-dimensional Klausmeier model, where autotoxicity effects are also taken into account. As the system moves away from the wave bifurcation threshold, two classes of solutions arise: small-amplitude periodic migrating bands near onset and large-amplitude travelling pulses in far-from-equilibrium conditions. For the first class, results of LSA reveal that inertia has a twofold role at onset: it acts as a destabilising mechanism, thereby enlarging the parameter region in which uphill migrating vegetation bands can emerge, and it reduces the pattern migration speed. Its role also manifests itself close to onset, as proved by the Stuart-Landau equation for the pattern amplitude deduced via multiple-scale WNA. Indeed, it is shown that inertial effects may reverse the dynamical regime, from supercritical to subcritical, thus leading to hysteresis. For the second class of solutions, the travelling vegetation pulses are first captured via numerical simulations and then investigated via Geometric Singular Perturbation Theory (GSPT). In far-from-equilibrium conditions, inertia is shown to increase pulse speed while preserving the intrinsic multiscale structure of the solution, in full agreement with the numerical findings. Overall, the proposed combined analytical-numerical investigations have depicted several ecological scenarios as a function of the distance from the instability threshold, elucidating that inertia does not exclusively act as a time lag.

研究动机与目标

• 研究惯性效应如何影响坡坡陆 semi-arid 草地上植被格局的形成与演化。
• 在从接近起始到远离平衡的区域特征化格局类型。
• 引入自毒效应并评估其与惯性与降雨的相互作用。
• 开发并应用解析与数值技术的混合方法，以绘制格局区和转变。

提出的方法

• 将带有自毒性的 Klausmeier 模型进行双曲（含惯性）的推广（无量纲形式见 Eq. 2–4）。
• 在沙漠态和绿地稳态周围进行线性稳定性分析，以确定波不稳定性的起始（波分岔轨迹）。
• 应用多尺度弱非线性分析，导出近起始处的 Stuart–Landau 型振幅方程。
• 使用几何奇点扰动理论构建并分析远离起始的大振幅行进脉冲。
• 用数值模拟（如 COMSOL）验证理论发现，探究格局形成与脉冲动力学。
• 求解简化/层解（Eq. 16–17），以确定迁移速度和起始时的临界降雨阈值。

Figure 1: Subdivision of the $\left(\mathcal{B},\mathcal{A}\right)$ -plane into three different zones according to the location of the existence threshold $\mathcal{A}=\mathcal{A}_{ex}$ and the wave bifurcation locus $\mathcal{A}=\mathcal{A}_{c}$ obtained via numerical integration of System ( 16 )-(

实验结果

研究问题

• RQ1 惯性如何改变波不稳定性的起始及模式的迁移速度？
• RQ2 哪些参数区间在接近起始处出现迁移带，而在远离起始处出现行进脉冲？
• RQ3 惯性是否促成亚临界分岔和格局形成的迟滞？
• RQ4 自毒性和降雨如何与惯性相互作用以塑造格局形态与动态？

主要发现

• 惯性扩大了格局形成区域，并在起始附近可能放慢迁移速度，起到去稳定化的作用。
• 惯性可能引发从超临界到亚临界分岔的转变，从而在格局形成中产生迟滞。
• 远离起始时，惯性增加行进脉冲的速度并保持脉冲的多尺度结构。
• 出现两大格局类别：在接近起始处的小振幅迁移带，以及在远离平衡处的大振幅行进脉冲。
• 增大惯性会扩大格局形成区域，尤其在较高降雨时更为明显。
• 起始时的迁移速度在数值与解析结果中保持一致，惯性影响速度并对自毒性敏感性进行调节。

Figure 2: Vegetation pattern dynamics observed into the wave instability region under worsening environmental conditions for increasing aridity (panels a-d) and increasing plant mortality (panels e-h). Panels (a) and (h) show the spatio-temporal evolution of the patterned solution obtained by sweepi