细胞内钙浓度的随机模型

中文摘要 AI 辅助

本文在随机框架下研究细胞内钙浓度（ICC）的慢-快模型，其中引入随机扰动以捕捉此类生物系统的内在随机性。我们首先分析基于FitzHugh-Nagumo结构的三维单细胞模型，随后将分析扩展到耦合的双细胞六维系统。我们证明了解的存在性和唯一性，并建立了钙变量的正性。我们获得了确定性平衡点附近的显式均方稳定性估计，并量化了它们对噪声强度的依赖。对单细胞和耦合系统的数值模拟展示了相关的定性行为，并揭示了随机框架中出现的额外动力学特征。

英文摘要

In this paper, we study a slow-fast model of Intracellular Calcium Concentrations (ICC) within a stochastic framework, where stochastic perturbations are introduced to capture the intrinsic randomness of such biological systems. We first analyse the three-dimensional single-cell model, based on the FitzHugh-Nagumo structure, and subsequently extend the analysis to a coupled two-cell six-dimensional setting. We prove existence and uniqueness of solutions and establish positivity of the calcium variable. We obtain explicit mean-square stability estimates around deterministic equilibria and quantify how they depend on the noise intensity. Numerical simulations for both the single-cell and coupled systems illustrate relevant qualitative behaviours and reveal additional dynamical features arising in the stochastic framework.

发表机构

• Wenzhou University（温州大学）
• Universidad de Sevilla（塞维利亚大学）

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