Global Stability and Sensitivity Analysis of a Delayed Nutrient-Plankton Model Under Climate Change and Oceans Deoxygenation

Abstract

Ocean deoxygenation driven by climate change and nutrient enrichment threatens marine ecosystems. This study analyzes a six-compartment nutrient-plankton-oxygen model incorporating three time-delays. Global asymptotic stability of the coexistence equilibrium is proved using the Lyapunov–Krasovskii method, indicating intrinsic ecosystem resilience. A novel threshold metric, the concentration number is derived via next-generation matrix techniques, signaling significant bloom-induced deoxygenation risk. Sensitivity analysis identifies nutrient-to-phytoplankton conversion ( ), nutrient uptake by phytoplankton ( ), and external nutrient input ( ) as strong positive drivers (+1.0 indices), while washout ( = −0.8) and phytoplankton mortality ( = −0.2) exert mitigating effects. Results show that plankton-mediated oxygen production and greenhouse gas removal provide stabilizing feedback sufficient to offset warming-induced oxygen losses under the parameter values considered. These findings highlight nutrient management and plankton conservation as critical strategies to mitigate climate-driven ocean deoxygenation and preserve marine ecosystem sustainability.