论文标题
局部渐近稳定性的局部差异方程系统，描述了突变下自我更新细胞种群克隆进化
Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation
论文作者
论文摘要
在本文中，我们考虑了一个非线性透气差异方程（IDE）的系统，该系统描述了经受突变和克隆选择的恶性白细胞（白血病细胞）的克隆异质种群的演变。我们证明了非平凡稳态的存在和独特性，并研究了它们的渐近稳定性。将结果与无突变的系统的结果进行比较。通过将稳态问题提出为特征值问题，并将Krein-Rutmann定理的版本应用于Banach Lattices来证明平衡的存在。使用线性化和Weinstein-Aronszajn决定因素分析平衡时的稳定性，该决定因素允许结论局部渐近稳定性。
In this paper we consider a system of non-linear integro-differential equations (IDEs) describing evolution of a clonally heterogeneous population of malignant white blood cells (leukemic cells) undergoing mutation and clonal selection. We prove existence and uniqueness of non-trivial steady states and study their asymptotic stability. The results are compared to those of the system without mutation. Existence of equilibria is proved by formulating the steady state problem as an eigenvalue problem and applying a version of the Krein-Rutmann theorem for Banach lattices. The stability at equilibrium is analysed using linearisation and the Weinstein-Aronszajn determinant which allows to conclude local asymptotic stability.
