On balanced optimal growth and development of biomass vegetation

A mathematical model for the distribution of photosynthesis assimilates directed to the growth and respiration of the biomass of leaves, roots, and reproductive organs of plants is formulated. It is associated with a model of transfer heat, moisture and CO2 in the natural plant cover (PC) and soil, taking into account the energy balance. With the help of growth functions that control the assimilates distribution, the problem of maxi mizing the final value of the biomass of the reproductive organs of plants in the PC at a given time interval is studied. In the model, the specific power function of photosynthesis depends on the ratio of the biomass of leaves and roots and has a single maximum. For a constant medium, it is proved that a linear control problem has a special solution-а balanced growth of biomasses of the PC in the vegetative phase with a constant ratio of the biomass of leaves and roots. The solution defines and explicitly describes three phases: initial, vegetative and reproductive, which makes it possible for each phase to obtain rather simple mathematical models of growth and development of the biomass of the PC, convenient for research and application: for identification, description of the water regime, evaluation of the PC water consumption etc. The work is of interest to the application of methods of optimal control theory to modeling problems.