# BSU bulletin. Mathematics, Informatics

Bibliographic description:
Vorotyntsev A. V.
О СБАЛАНСИРОВАННОМ ОПТИМАЛЬНОМ РОСТЕ И РАЗВИТИИ БИОМАСС РАСТИТЕЛЬНОГО ПОКРОВА // BSU bulletin. Mathematics, Informatics. - 2018. №3. . - С. 72-84.
Title:
О СБАЛАНСИРОВАННОМ ОПТИМАЛЬНОМ РОСТЕ И РАЗВИТИИ БИОМАСС РАСТИТЕЛЬНОГО ПОКРОВА
Financing:
Codes:
DOI: 10.18101/2304-5728-2018-3-72-84UDK: 519.87
Annotation:
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 photosyn- thesis depends on the ratio of the biomass of leaves and roots and has a single maxi- mum. For a constant medium, it is proved that a linear control problem has a special solution-a balanced growth of biomasses of the PC in the vegetative phase with a con- stant ratio of the biomass of leaves and roots. The solution defines and explicitly de- scribes 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, de- scription 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 prob- lems.
Keywords:
modeling of the plant cover; distribution of photosynthesis assimilates; growth functions; optimal balanced growth.
List of references:
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Vorotyntsev A. V. Model' perenosa tepla i vlagi v sisteme pochva-rastenie s uche- tom balansa energii [Model of Heat and Moisture Transfer in the Soil-Plant System Taking into Account the Energy Balance]. Vestnik Buryatskogo gosudarstvennogo uni- versiteta – Bulletin of Buryat State University. 2012. No. 1. Pp. 107–111.

Vorotyntsev A. V. Issledovanie modeli vodno-teplovogo rezhima sistemy pochva-rastenie-prizemnyi sloi vozdukha [Research of the Model of Water-Heat Re- gime of the Soil-Plant-Surface Air Layer System]. Moscow: Computing Center of RAS, 1991. 53 p.

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Vorotyntsev A. V. Priblizhennaya model' perenosa tepla i vlagi v sisteme pochva-rastenie s uchetom balansa energii [Approximate Model of Heat and Moisture Transfer in the Soil-Plant System Taking into Account the Energy Balance]. Vestnik Buryatskogo gosudarstvennogo universiteta. Matematika, Informatika – Bulletin of Buryat State University. Mathematics, Informatics. 2014. Issue 9, No. 1. Pp. 22–26.

Vorotyntsev A. V., Rogozhina N. L., Sokolova I. A., Stepchenkova S. O. Dve zadachi optimal'nogo upravleniya dlya modeli sistemy pochva-rastenie [Two Optimal Control Problems for the Soil-Plant System Model].Moscow: Computing Center of AS USSR, 1988. 38 p.

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Vorotyntsev A. V. Model' raspredeleniya assimilyatov i optimal'nogo rosta ras- titel'nogo pokrova [Model of Distribution of Assimilates and Optimal Growth of Vegetation Cover]. Vestnik Buryatskogo Gosudarstvennogo Universiteta. Matematika, Informatika – Bulletin of Buryat State University. Mathematics, Informatics. 2015. Issue 9. Pp. 54–61.