Qualitative analysis and stability of the dynamics of photosynthesis in autotrophic systems

A nonlinear system of three differential equations is studied that describes photosynthesis in autotrophic systems. An area is identified that is invariant with respect to motion along the trajectory of the system with increasing time. In this area, the existence of a unique stationary solution is established and questions of its stability are investigated. At present, due to the exponential growth of the population, industrial progress and, as a consequence, an increase in the general pollution of the biosphere, the study of the resistance of plant organisms to anthropogenic pollution is acquiring the most important practical and theoretical significance. At the same time, the problem of a qualitative study of the processes of photosynthesis has become extremely urgent. In problems related to photosynthesis, it is of great interest to determine the laws of functioning of the system, as well as the choice of methods of mathematical and computer modeling. This is the process of converting the absorbed light energy into chemical energy of organic compounds, the only process in the biosphere leading to an increase in the energy of the biosphere due to an external source — the Sun, which ensures the existence of both plants and all heterotrophic organisms. The most important external factors affecting the processes of photosynthesis and photorespiration are temperature, photosynthetic active radiation, water regime, the regime of plant mineral nutrition, as well as the content of carbon dioxide and oxygen in the surrounding space. In recent decades, there has been an increase in the concentration of carbon dioxide in the atmosphere and a change in the thermal regime on a planetary scale. In this regard, the problem of predicting changes in the intensity of photosynthesis of plants caused by changes in the concentration of atmospheric carbon dioxide and temperature is urgent.