Institute of Automation and Control Processes, FEB RAS, Vladivostok, Russia

Abstract. Droop's well-known model simulates phytoplankton biomass dynamics based on nutrient limitation. The defining parameter is the nutrient concentration in phytoplankton cells (cell quota). This model is modified to description of the photosynthesis processes. The effects of photosynthetically active radiation must be taken into account. At the same time, the nutritional factor remains the main one. Water temperature is considered as a controlling factor. The influence of light during photosynthesis plays a decisive role. The decisive factor is the presence of photosynthetic substances. We conventionally combine them under the name "chlorophyll". Sufficient variability in the proportion of chlorophyll in phytoplankton (chlorophyll quota) directly affects biomass production. The equation for the dynamics of chlorophyll quota is added to the Droop model. The parameters of the model depend on the concentration of nutrients, illumination and water temperature. The properties of the solutions in the model are investigated, the conditions for the existence and stability of equilibrium solutions are clarified. Complex dynamic regimes are revealed in the case of unstable equilibria. It was found that the most sensitive parameter for biomass dynamics is the minimum value of the cell quota. The dynamics of indicators for the daily cycle and the annual cycle of seasonal changes are calculated. The influence of nutrition, illumination and temperature on biomass production has been clarified. During the day, the chlorophyll quota fluctuates insignificantly due to a short period of time. The changes are noticeable at longer times for example during the season.

Key words: phytoplankton, photosynthesis, chlorophyll, mathematical model, nutrition, illumination, temperature, cell quota.