Abstract
Abstract
This study presents a new mathematical model of the physiology of the plant open system development in the conditions far from equilibrium. Unlike existing approaches, our model is based on the equations describing competition for the substrate between the three main compartments of cultivated plants - the root, stem and leaf system in extreme conditions. Exchange with the external environment occurs through two channels - through the leaves and the root system. The internal control channel is defined as a function of limiting the plant biomass through the biomass of the individual structural parts. The model viability was tested on the example of physiological model of tomato development. The system’s behavior was studied under two varieties of extreme conditions - a lack of nutrients in the soil and a low level or lack of solar radiation. In the first case, the model shows the restructuring of the system after several levels of vibrations to a stable state with a low consumption of substrate and a redistribution of the leaves, stem and root masses. In the second case, the calculations show a significant suppression of leaf cover biomass and mass redistribution in favor of the stem and root. However, even in this case, after a period of instability, the system comes to a stable state with the mass of the stem exceeding the mass of other structures. For each case, phase trajectories of the biomass and substrates behavior are constructed.