Abstract

Vegetation community plays a pivotal role in various geomorphic processes. The growth of vegetation intrinsically depends on the effective shear stresses exerted by the flow of material (e.g., water or soil) along the slope. We comparatively assess the growth and decay of vegetation using linear and logistic growth model coupled with a runoff erosion model. The linear growth model predicts a sharp decrease in the non-dimensional vegetation profile from the upper reach to the lower part along the slope. However, the logistic growth model delivers a smooth gradual decrease in the vegetation extent. Additionally, we propose a stochastic model to capture the role of internal and external factors in the dynamics of vegetation growth using two Gaussian noises. The steady probability distribution functions from the stochastic model provide insights about the role of different noises on the reaction of the system and suggest that bio-environmental factors are difficult to segregate from one another.

Highlights

• Comparative study between logistic and linear vegetation growth model coupled with a surface erosion model.

• Steady-state equilibrium vegetation profile along any slope suggests that the logistic growth model is more realistic.

• Effect of Gaussian noises in vegetation growth has been demonstrated with the aid of stationary probability distribution.

中文翻译：

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噪声诱发系统中植被生长的稳定性

摘要

植被群落在各种地貌过程中起着举足轻重的作用。植被的生长本质上取决于沿斜坡的物质（例如水或土壤）流动所施加的有效切应力。我们使用线性和逻辑增长模型以及径流侵蚀模型比较评估植被的生长和衰退。线性增长模型预测，无量纲植被剖面将从上游到下部沿着陡坡急剧减少。但是，逻辑增长模型可以使植被范围逐渐平滑地减少。此外，我们提出了一种随机模型，利用两个高斯噪声来捕获内部和外部因素在植被生长动态中的作用。

强调

• Logistic和线性植被生长模型与表面侵蚀模型之间的比较研究。

• 沿任何斜坡的稳态平衡植被剖面表明，逻辑增长模型更为现实。

• 高斯噪声对植被生长的影响已借助平稳概率分布得到了证明。