Geodesic
Qualitative analysis and stability of the dynamics of photosynthesis in autotrophic systems
Vladikavkazskij matematičeskij žurnal, Tome 23 (2021) no. 3, pp. 114-125 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{VMJ_2021_23_3_a8,
     author = {E. M. Mukhamadiev and I. D. Nurov and Z. I. Sharifzoda},
     title = {Qualitative analysis and stability of the dynamics of photosynthesis in autotrophic systems},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {114--125},
     year = {2021},
     volume = {23},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2021_23_3_a8/}
}
TY  - JOUR
AU  - E. M. Mukhamadiev
AU  - I. D. Nurov
AU  - Z. I. Sharifzoda
TI  - Qualitative analysis and stability of the dynamics of photosynthesis in autotrophic systems
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2021
SP  - 114
EP  - 125
VL  - 23
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMJ_2021_23_3_a8/
LA  - ru
ID  - VMJ_2021_23_3_a8
ER  - 
%0 Journal Article
%A E. M. Mukhamadiev
%A I. D. Nurov
%A Z. I. Sharifzoda
%T Qualitative analysis and stability of the dynamics of photosynthesis in autotrophic systems
%J Vladikavkazskij matematičeskij žurnal
%D 2021
%P 114-125
%V 23
%N 3
%U http://geodesic.mathdoc.fr/item/VMJ_2021_23_3_a8/
%G ru
%F VMJ_2021_23_3_a8
E. M. Mukhamadiev; I. D. Nurov; Z. I. Sharifzoda. Qualitative analysis and stability of the dynamics of photosynthesis in autotrophic systems. Vladikavkazskij matematičeskij žurnal, Tome 23 (2021) no. 3, pp. 114-125. http://geodesic.mathdoc.fr/item/VMJ_2021_23_3_a8/

[1] Riznichenko G. Yu., Lektsii po matematicheskim modelyam v biologii, Izd-vo «Regulyarnaya i khaoticheskaya dinamika», M.–Izhevsk, 2011, 558 pp.

[2] Rubin A. B., Biofizika, v. 2, Biofizika kletochnykh protsessov, 2-izd., Izd-vo MGU, M., 2000, 468 pp.

[3] Riznichenko G. Yu., Belyaeva N. E., Kovalenko I. B., Rubin A. B., “Matematicheskoe i kompyuternoe modelirovanie pervichnykh protsessov fotosinteza”, Biofizika, 54:1 (2009), 16–33

[4] Nurov I. D., Sharifzoda Z. I., “Kachestvennoe issledovaniya sistemy kineticheskikh uravnenii, opisyvayuschikh vzaimodeistvie odnoelektronnogo i dvukhelektronnogo perenoschika”, XXVI Mezhdunar. konf. «Matematika. Kompyuter. Obrazovanie» (g. Puschino, 28 yanvarya — 2 fevralya 2019 g.), 2019, 17

[5] Mukhamadiev E. M., Sharifzoda Z. I., Nurov I. D., “Kachestvennye issledovaniya nelineinoi zadachi fotosinteza”, Dokl. AN Resp. Tadzhikistan, 62:9–10 (2019), 511–518

[6] Kurosh A. G., Kurs vysshei algebry, Nauka, M., 1968, 431 pp. | MR

[7] Bautin N. N., Leontovich E. A., Metody i priemy kachestvennogo issledovaniya dinamicheskikh sistem na ploskosti, Nauka, M., 1976, 496 pp.

[8] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970, 720 pp.

[9] Arabov M. K., “Analiz ustoichivosti osoboi tochki kvazilineinogo uravneniya vtorogo poryadka”, Izv. AN Resp. Tadzhikistan. Otd. fiz.-mat., khim., geol. i tekhn. nauk, 158:1 (2015), 42–49

[10] Ilolov M., Kuchakshoev Kh. S., “Ob abstraktnykh uravneniyakh s neogranichennymi nelineinostyami i ikh prilozheniya”, Dokl. AN, 428:3 (2009), 310–312 | MR | Zbl

[11] Mukhamadiev E. M., Nurov I. D., Khalilova M. Sh., “Predelnye tsikly kusochno-lineinykh differentsialnykh uravnenii vtorogo poryadka”, Ufim. mat. zhurn., 6:1 (2014), 84–93 | MR

[12] Mukhamadiev E. M., Gulov A. M., Nurov I. D., “Analiz rozhdeniya predelnykh tsiklov odnogo klassa nelineinoi uravnenii vtorogo poryadka”, Vestn. Voronezh. gos. un-ta. Ser. Fizika. Matematika, 2016, no. 1, 118–125 | MR

[13] Yumagulov M. G., Vvedenie v teoriyu dinamicheskikh sistem, Ucheb. posobie, Lan, SPb., 2015, 272 pp.

[14] Gulov A. M., Sharifzoda Z. I., Certification: That they are the authors of the computer program of the “A software package for constructing phase portraits of dynamic systems”, 21.06.2019