植被斑图动力学系统的参数反演  

Parameter Identification of Vegetation Pattern Dynamic System

作　　者：罗心悦 陈瑜 LUO Xinyue;CHEN Yu(School of Mathematical Sciences,Fudan University,Shanghai 200433,China;School of Mathematics,Shanghai University of Finance and Economics,Shanghai 200433,China)

机构地区：[1]复旦大学数学科学学院,上海200433 [2]上海财经大学数学学院,上海200433

出　　处：《复旦学报（自然科学版）》2022年第3期323-334,共12页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金项目(11971121)。

摘　　要：基于生态学背景与反应扩散方程理论,建立带有土壤水扩散反馈调节机制的平地植被斑图演化模型。利用半隐式Euler方法计算得到在2维情况下的斑图模式解。数值模拟表明降水量、植物死亡率的反馈效应促成了植被斑图的形成与演化。针对具有终时观测的参数反演问题,本文应用变步长梯度算法得到有效的参数估计。此外,本文基于贝叶斯反问题理论,提出一种系统参数反演的新策略,可实现观测间断情况下系统参数的最大后验概率估计。Vegetation patterns characterize the distribution of the vegetation and provide some signs for vegetation protection.To reveal the mechanism and evolution of vegetation pattern formation,a water-biomass model in semi-arid environments with soil-water diffusion feedback is established.The numerical simulation demonstrates that rainfall and plant loss contribute to pattern transition.To solve the parameter identification problem with final-time observation,we apply the variable-step gradient algorithm to estimate parameters.For more general real-world situations,a new approach of parameter identification is proposed.This method is based on the idea of data assimilation and obtain the MAP estimation of parameters with data from discrete observations.

关 键 词：植被斑图 反应扩散系统 参数反演 

分 类 号：Q948[生物学—植物学] O29[理学—应用数学]