Aquatic Ecology and Water Environment Safety

CLC number: O175.13

Global Stability of Aquatic Ecosystems with Terrestrial Organic Carbon

具有陆地有机碳输入的水生生态系统全局稳定性

School of Mathematics and Statistics, Weinan Normal University, Weinan 714099, Shaanxi, China (渭南师范学院　数学与统计学院,　陕西　渭南　714099)

Received: 2 May 2025

Abstract

To quantitatively analyze the physical and biological dynamics of terrestrial organic carbon (TOC), phytoplankton, and zooplankton, and to clarify the relationship between global stability and the input TOC concentration, this paper proposes a mathematical model for aquatic ecosystems. The interactive dynamics are analyzed by using Hurwitz’s criterion, LaSalle’s invariance principle, and appropriate Lyapunov functions. Key results show that the phytoplankton-free equilibrium is globally asymptotically stable at high input TOC concentrations. In contrast, the coexisting equilibrium exhibits global asymptotic stability under low input TOC conditions. These theoretical findings are validated by numerical simulations, highlighting the importance of monitoring and regulating input TOC concentrations to preserve biodiversity.

摘要

为定量解析陆地有机碳(TOC)、浮游植物与浮游动物的动力学过程，揭示平衡点的全局稳定性与TOC输入浓度的内在关联，本文构建了水生生态系统的数学模型。借助Hurwitz判据、LaSalle不变性原理及适配的Lyapunov函数，系统地分析了模型的交互动力学特性。研究发现：当TOC输入浓度处于较高水平时，无浮游植物平衡点呈现全局渐近稳定性；而在低浓度TOC输入条件下，系统共存平衡点表现出全局渐近稳定性。数值模拟结果进一步验证了理论结论，明确了监测与调控TOC输入浓度对维系水生生物多样性的关键意义。