一类描述自更新细胞群体克隆进化的积分微分方程系统的局部渐近稳定性
Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation
摘要：
在本文中，我们考虑一个系统的非线性积分微分方程（IDES）描述的恶性白细胞（白血病细胞）的克隆非齐性总体的突变和克隆选择的演变。证明了非平凡平衡态的存在唯一性，并研究了其渐近稳定性。将结果与无突变系统的结果进行了比较。平衡点的存在性证明了制定的稳定状态问题作为一个本征值问题和应用版本的Krein-Rutmann定理的巴拿赫格。使用线性化和Weinstein-Aronszajn行列式分析平衡时的稳定性，从而得出局部渐近稳定性的结论。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
