Models of soil organic carbon (SOC) frequently overlook the effects of spatial dimensions and microbiological activities. In this paper, we focus on two reaction-diffusion chemotaxis models for SOC dynamics, both supporting chemotaxis-driven instability and exhibiting a variety of spatial patterns as stripes, spots and hexagons when the microbial chemotactic sensitivity is above a critical threshold. We use symplectic techniques to numerically approximate chemotaxis-driven spatial patterns and explore the effectiveness of the piecewice dynamic mode decomposition (pDMD) to reconstruct them. Our findings show that pDMD is effective at precisely recreating chemotaxis-driven spatial patterns, therefore broadening the range of application of the method to classes of solutions different than Turing patterns. By validating its efficacy across a wider range of models, this research lays the groundwork for applying pDMD to experimental spatiotemporal data, advancing predictions crucial for soil microbial ecology and agricultural sustainability.

翻译：土壤有机碳（SOC）模型常忽视空间维度与微生物活动的影响。本文聚焦于两个描述SOC动态的反应-扩散趋化模型，二者均支持趋化性驱动的不稳定性，并在微生物趋化敏感性超过临界阈值时呈现出条纹、斑点及六边形等多种空间模式。我们采用辛技术对趋化性驱动的空间模式进行数值逼近，并探究分段动态模态分解（pDMD）方法重建这些模式的有效性。研究结果表明，pDMD能有效精确重构趋化性驱动的空间模式，从而将该方法的适用范围拓展至图灵模式之外的其他解类。通过在更广泛的模型中验证其效能，本研究为将pDMD应用于实验时空数据奠定了基础，推进了对土壤微生物生态与农业可持续性至关重要的预测研究。