分数阶Logistic模型的差分解与环境容纳量反演  

Finite Difference Solution for a Fractional-order Logistic Model and Inversion of Carrying Capacity

作　　者：李怡璇 贾现正 李功胜 LI Yixuan;JIA Xianzheng;LI Gongsheng(School of Math and Statistics,Shandong University of Technology,Zibo 255049,China)

机构地区：[1]山东理工大学数学与统计学院,山东淄博255049

出　　处：《郑州大学学报（理学版）》2024年第2期87-94,共8页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金项目(11871313);山东省自然科学基金项目(ZR2019MA021)。

摘　　要：对于具有空间依赖环境容纳量的分数阶Logistic非线性增长模型,通过变量替换建立有限差分格式,在环境容纳量适当大的条件下,利用谱估计方法证明差分格式的稳定性和收敛性。进而考虑一个利用内点观测数据重建环境容纳量的反问题,应用同伦正则化算法进行数据随机扰动下的数值反演,计算结果表明反演重建解随着扰动水平的减小逐步逼近真解。The problem of a nonlinear fractional-order Logistic model with space-dependent carrying capacity was solved.A finite difference scheme for the forward problem was established,and its stability and convergence were proved based on the estimate of the spectral radius of the coefficient matrix with large capacities.An inverse problem of reconstructing the capacity function with additional measurements at one interior point was solved by the homotopy regularization algorithm,and numerical inversions with noisy data were presented to demonstrate the efficiency of the numerical method.

关 键 词：分数阶Logistic模型 环境容纳量 有限差分格式 稳定性与收敛性 反问题 数值反演 

分 类 号：O175[理学—数学]