**Mathematical Model of Phytoplankton Interspecific Competition for Food Resource**
**Abakumov A.I., Kozitskaya I.S.**
*Institute of Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia*

**Abstract**. The phytoplankton in an aquatic ecosystem is the basis of its life activity and the main producing link. The functioning of phytoplankton in same time depends on environmental factors: mineral nutrition, photosynthetically active solar radiation, water temperature and other less significant ones. Sunlight is a stable factor, varying predictably over time and space. The water temperature is the small regulatory factor. Concentrations of mineral substances can change quite quickly and significantly, this much influences on plant organisms. Thus, mineral nutrition is a basic environmental factor of influence to phytoplankton. On the other hand, in large aquatic basin such as seas and oceanic areas the distribution of living organisms is very heterogeneous in space. These two aspects – nutrient and spatial heterogeneity – are the focus of this article. A model of competitive interaction is considered using the example of two species of phytoplankton. The phytoplankton move passively in water what is simulated by the diffusion process. The model contains one non-trivial stationary and spatially homogeneous equilibrium and two trivial ones, i.e. degenerate in at least one species of phytoplankton. Trivial equilibria are stable only in some “degenerate” situations. The non-trivial equilibrium in “normal” conditions is stable to temporal and spatial disturbances. The behavior of solutions near a nontrivial equilibrium for a stationary living environment and in cases of its nonstationary is studied. Perturbation of a nontrivial equilibrium in a stationary environment leads to relatively long-term deviations from equilibrium and a slow return to it. The instability of trivial equilibria increases the spatial heterogeneity of solutions. At the same time, the nontrivial equilibrium computationally demonstrates weak properties of global stability in time. The unsteadiness of the environment is simulated by the unsteadiness of the influx of nutrients. It has been shown that the distribution of nutrients can lead to significant heterogeneity in the distribution of individuals across the spatial habitat.

**Key words**: *mathematical model, phytoplankton, diffusion, nutrient, stability, spatial heterogeneity.*