AI 中文总结
研究非局部耦合合作系统主谱理论，通过置换矩阵重排算子分量分解为子算子，刻画谱界。基于此给出非局部扩散系统基本再生数变分特征，分析多基因型干细胞再生模型动力学行为及非强耦合时的阈值动力学。
AI 中文摘要
本文研究具有耦合扩散的非局部扩散算子的主谱理论，旨在为系统非强耦合情形建立谱界的变分特征。在此情形下，因主特征函数可能有恒为零的分量，现有广义特征值方法不适用。为此，用置换矩阵重新排列算子分量，分解为合适子算子，根据子算子谱界刻画原算子谱界。基于此主谱理论，给出非局部扩散系统基本再生数的变分特征，分析一类有表观遗传转变的多基因型干细胞再生模型在有无基因突变时的动力学行为，且不假设主特征值存在。此外，研究系统非强耦合时的阈值动力学。
英文摘要
This paper investigates the principal spectral theory of a nonlocal dispersal operator with coupled diffusion and aims to establish a variational characterization of the spectral bound for the case where the system is not strongly coupled. In this setting, a key difficulty arises since the principal eigenfunction may have components that are identically zero, rendering existing generalized eigenvalue methods inapplicable. To overcome this, we reorder the components of the operator using a permutation matrix, thereby decomposing it into suitable suboperators, and characterize the spectral bound of the original operator in terms of the spectral bounds of these suboperators. Building on this principal spectral theory, we provide a variational characterization of the basic reproduction ratio for nonlocal dispersal systems and analyze the dynamical behavior of a class of multi-genotype stem cell regeneration models with epigenetic transitions, both in the presence and absence of gene mutations, without assuming the existence of a principal eigenvalue. Furthermore, we investigate the threshold dynamics when the system is not strongly coupled.
Comments30 pages, 3 figures
