Asymptotic and Transient Dynamics of a Stoichiometric Algal Growth Model with Two-Stage Phosphate Uptake

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-08-02 DOI:10.1137/23m1611750

Shufei Gao, Sanling Yuan, Anglu Shen, Hao Wang

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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1668-1696, August 2024.
Abstract. Exploring the mechanism of phosphate ([math]) uptake by algae is essential to accurate prediction and a comprehensive understanding of harmful algal blooms (HABs). Previous experimental studies have revealed the existence of two distinct [math] pools, namely the surface-adsorbed [math] pool and the intracellular [math] pool, in certain species of algae. Motivated by these observations, a novel stoichiometric model, which incorporates a two-stage [math] uptake process, is proposed and analyzed to investigate the impact of these [math] pools on algal growth. Model validation results show that with proper parameterizations, this model can accurately capture algal growth dynamics in the laboratory and in the field. The asymptotic dynamics are explored through a complete mathematical analysis and the transient dynamics are explored through multiscale analysis, revealing the driving mechanism of different growth phases of algae. Furthermore, we derive an approximate formula for estimating the switching time from high to low growth rate in algae, which can serve as a valuable tool for predicting the duration of HABs. These findings contribute to the strengthening of prediction and improving understanding of HABs.

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具有两阶段磷酸盐吸收的定量藻类生长模型的渐近和瞬态动力学分析

SIAM 应用数学期刊》，第 84 卷第 4 期，第 1668-1696 页，2024 年 8 月。摘要。探索藻类吸收磷酸盐（[math]）的机理对于准确预测和全面了解有害藻华（HABs）至关重要。以往的实验研究发现，某些藻类存在两个不同的[math]池，即表面吸附的[math]池和细胞内的[math]池。受这些观察结果的启发，我们提出并分析了一个包含两阶段[math]吸收过程的新型化学计量模型，以研究这些[math]池对藻类生长的影响。模型验证结果表明，只要参数设置得当，该模型就能准确捕捉实验室和野外的藻类生长动态。我们通过完整的数学分析探讨了渐近动力学，并通过多尺度分析探讨了瞬态动力学，揭示了藻类不同生长阶段的驱动机制。此外，我们还推导出估算藻类从高生长率到低生长率切换时间的近似公式，该公式可作为预测 HABs 持续时间的重要工具。这些发现有助于加强对 HABs 的预测和理解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.