基于改进Klausmeier模型的交叉对流对斑图形成的影响研究

Research on the Effects of Cross-Advection on Pattern Formation Based on Modified Klausmeier Model

摘要: 为了研究交叉对流项对斑图形成的影响，将缓坡上植被种子随水流动的效应，通过交叉对流项引入一个改进的Klausmeier模型。对模型进行无量纲化后，求解了其空间均匀定态解以及稳定性。基于稳定的均匀定态解，进行了图灵分岔分析，揭示交叉对流项对图灵分岔的影响。使用分岔图和斑图形成的模拟，验证理论分析的结果。结果显示，交叉对流项使得系统发生分岔的难度改变，使得系统形成稳定带状斑图的速度更快，但形成的植被带移动速度降低。

Abstract: In order to investigate the effects of cross-advection on pattern formation, the effects of vegetation seed dispersal along with hillslope runoff were considered as a cross-advection term in a modified Klausmeier model. After the nondimensionalization of the model, its spatially homogeneous steady states of the model and the corresponding stability are solved. Based on the stable homogeneous steady states, Turing bifurcation analysis was performed to reveal the effects of cross-advection on Turing bifurcation. Bifurcation diagram and simulation of pattern formation were obtained to verify the theoretical results. The results show that with the cross-advection, the difficulty of Turing bi-furcation occurrence varies, and the formation of stable banded patterns becomes faster, but the propagation velocity of vegetation bands decreases.