$\u211d^2$ 中细胞-体 ODE-PDE 模型的同步记忆依赖细胞内振荡
Synchronized Memory-Dependent Intracellular Oscillations for a Cell-Bulk ODE-PDE Model in $\mathbb{R}^2$
AI总结：
本文针对 $\u211d^2$ 中细胞-体 ODE-PDE 模型，利用强局部化摄动理论和指数和法建立快速算法，研究记忆依赖体扩散场中的细胞内振荡同步，并在 Sel'kov 动力学下展示了相位同步、混合模式振荡和群体感应等现象。
摘要：
针对 $\u211d^2$ 中的细胞-体 ODE-PDE 模型，本文发展了一种混合渐近-数值理论，为研究空间分离的动态活跃“单元”或“细胞”相关的振荡动力学如何受到由整个细胞群产生和吸收的 PDE 体扩散场的调控，提供了一种新的理论且计算高效的方法。在 PDE 扩散场中研究振子同步是 Yoshiki Kuramoto 奠基性工作的最初目标之一。对于该细胞-体模型，本文使用强局部化摄动理论并将其扩展到时间依赖情形，推导出一个新的积分-微分 ODE 系统，用以刻画记忆依赖体扩散场中的细胞内动力学。针对这一非局部约化系统，本文发展了一种新颖的快速时间推进格式，该格式部分依赖于指数和法来数值处理卷积积分，从而能够在长时间区间上快速且准确地计算积分-微分系统的数值解。对于 Sel'kov 反应动力学的特殊情形，本文展示了多种大规模振荡动力学行为，包括相位同步、混合模式振荡和群体感应，这些行为对应于流入和流出渗透率参数、体降解速率和体扩散率以及细胞具体空间构型的各种取值范围。本文快速算法的结果在笔记本电脑上不到一分钟的 CPU 时间内即可获得，并与使用商业 PDE 求解器执行的细胞-体模型 PDE 模拟进行了基准对比，后者的运行时间高出数个数量级。
英文摘要：
For a cell-bulk ODE-PDE model in $\mathbb{R}^2$, a hybrid asymptotic-numerical theory is developed to provide a new theoretical and computationally efficient approach for studying how oscillatory dynamics associated with spatially segregated dynamically active ``units" or ``cells" are regulated by a PDE bulk diffusion field that is both produced and absorbed by the entire cell population. The study of oscillator synchronization in a PDE diffusion field was one of the initial aims of Yoshiki Kuramoto's foundational work. For this cell-bulk model, strong localized perturbation theory, as extended to a time-dependent setting, is used to derive a new integro-differential ODE system that characterizes intracellular dynamics in a memory-dependent bulk-diffusion field. For this nonlocal reduced system, a novel fast time-marching scheme, relying in part on the \emph{sum-of-exponentials method} to numerically treat convolution integrals, is developed to rapidly and accurately compute numerical solutions to the integro-differential system over long time intervals. For the special case of Sel'kov reaction kinetics, a wide variety of large-scale oscillatory dynamical behavior including phase synchronization, mixed-mode oscillations, and quorum-sensing are illustrated for various ranges of the influx and efflux permeability parameters, the bulk degradation rate and bulk diffusivity, and the specific spatial configuration of cells. Results from our fast algorithm, obtained in under one minute of CPU time on a laptop, are benchmarked against PDE simulations of the cell-bulk model, which are performed with a commercial PDE solver, that have run-times that are orders of magnitude larger.
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。
