Global Stability of Aquatic Ecosystems with Terrestrial Organic Carbon

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.