A Conceptual Nonlinear ODE Model for the Dynamics of Marine Heatwaves and Phytoplankton Blooms: Stability, Bifurcations, and Early Warning Signals

Marine heatwave (MHW) is the intense and long-term warming of the ocean waters which have increased two-fold since the 1980s and are disastrous to phytoplankton, the microscopic algae that produces half of the oxygen in the atmosphere and forms the base of the marine food web. To know how and why phytoplankton communities fail during thermal stress, the authors construct a four-dimensional nonlinear ODE of the relationships between sea surface temperature anomaly, nutrient concentration, phytoplankton biomass and cumulative thermal stress. Three biologically significant equilibria and a basic reproduction number R 0 whose intersection with unity initiates a transcritical bifurcation between ecosystem persistence and collapse are identified using mathematical analysis. Saddle-node bifurcations to give bistability and hysteresis are also identified in the model, as well as Hopf bifurcations to give boardwalk oscillation bloom dynamics. Most importantly, tipping points can be predicted by critical slowing down and increased variance, amplified autocorrelation and positive skewness with hundreds of simulation days of warning. These predictions are confirmed by numerical representation of three real MHW conditions, in which nutrient-poor (oligotrophic) waters are found to be particularly susceptible even in the case of relatively small temperature perturbations. The framework provides a strict but explainable scale of collapse risk quantification, implying that by monitoring the chlorophyll-a change and autocorrelation on the high-risk ocean areas, actionable, management-relevant early warnings of ecosystem collapse are possible.

Keywords: marine heatwaves, phytoplankton blooms, nonlinear ODE, bifurcation analysis, early warning signals, tipping points, critical slowing down, climate change, marine ecology, dynamical systems.