vmaitComputational Mathematics and Information TechnologiesComputational Mathematics and Information Technologies2587-8999Донской государственный технический университет10.23947/2587-8999-2019-2-2-83-103vmait-61Research ArticleСтатьиМатематическое моделирование нелинейных эффектов в динамике взаимодействия планктонных и рыбных популяций Азовского моряMathematical modeling of nonlinear effects in dynamic of interacting plankton and fish populations of Azov Seahttps://orcid.org/0000-0002-5875-1523СухиновАлександр ИвановичSukhinovAlexander Ivanovich

Сухинов Александр Иванович, Донской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1), доктор физико-математических наук, профессор

Sukhinov Alexander Ivanovich, Don State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation), Doctor of Science in Physics and Maths, Professor

sukhinov@gmail.comСидорякинаВалентина ВладимировнаSidoryakinaValentina Vladimirovna

Сидорякина Валентина Владимировна, Таганрогский институт им. А.П. Чехова (филиал) РГЭУ (РИНЭ) (347936 Таганрог, улица Инициативная, д. 48), кандидат физико-математических наук, доцент

Sidoryakina Valentina Vladimirovna, Taganrog Institute of A.P. Chekhov (branch) RSUE (Initiative Street, Taganrog, Russian Federation), Candidate of Science in Physics and Maths, Associate professor

cvv9@mail.ruhttps://orcid.org/0000-0001-7257-962XНикитинаАлла ВалерьевнаNikitinaAlla Valeryevna

Никитина Алла Валерьевна, Южный Федеральный Университет (347928, Россия, Ростовская область, г. Таганрог, пер. Некрасовский, 44), доктор технических наук, профессор

Nikitina Alla Valeryevna, Southern Federal University (Chekhov str., 2, Taganrog, Russian Federation), Doctor of Technical Science, Associate professor

nikitina.vm@gmail.comhttps://orcid.org/0000-0002-8323-6005ЧистяковАлександр ЕвгеньевичChistyakovAlexander Evgenievich

Чистяков Александр Евгеньевич, Донской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1), доктор физико-математических наук, доцент

Chistyakov Alexander Evgenievich, Don State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation), Doctor of Science in Physics and Maths, Associate professor

cheese_05@mail.ruФилинаАлёна АлександровнаFilinaAlena Aleksandrovna

Филина Алёна Александровна, Научно-исследовательский центр супер-ЭВМ и нейрокомпьютеров (347900, Россия, Ростовская область, г. Таганрог, пер. Итальянский, дом 106), кандидат технических наук, научный сотрудник

Filina Alena Aleksandrovna, Supercomputers and Neurocomputers Research Center, Co Ltd. (Italyansky lane, 106, Taganrog, Russian Federation), Candidate of Technical Science, Researcher

j.a.s.s.y@mail.ruhttps://orcid.org/0000-0001-8234-3194ЛитвиновВладимир НиколаевичLitvinovVladimir Nikolaevich

Литвинов Владимир Николаевич, Азово-Черноморский инженерный институт ФГБОУ ВО Донской ГАУ (РФ, г. Зерноград, ул. Ленина, 21), Кандидат технических наук, доцент.

Litvinov Vladimir Nikolaevich, Azov-Black Sea Engineering Institute of FSBEI HE Don State Agrarian University (21 Lenin st., Zernograd, Russian Federation), Candidate of Technical Sciences, Head of the Thermal Engineering and Information Management Systems department

litvinovvn@rambler.ruДонской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1)РоссияDon State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation)Russian FederationТаганрогский институт им. А.П. Чехова (филиал) РГЭУ (РИНЭ) (347936 Таганрог, улица Инициативная, д. 48)РоссияTaganrog Institute of A.P. Chekhov (branch) RSUE (Initiative Street, Taganrog, Russian Federation)Russian FederationЮжный Федеральный Университет (347928, Россия, Ростовская область, г. Таганрог, пер. Некрасовский, 44)РоссияSouthern Federal University (Chekhov str., 2, Taganrog, Russian Federation)Russian FederationНаучно-исследовательский центр супер-ЭВМ и нейрокомпьютеров (347900, Россия, Ростовская область, г. Таганрог, пер. Итальянский, дом 106)РоссияSupercomputers and Neurocomputers Research Center, Co Ltd. (Italyansky lane, 106, Taganrog, Russian Federation)Russian FederationАзово-Черноморский инженерный институт ФГБОУ ВО Донской ГАУ (РФ, г. Зерноград, ул. Ленина, 21)РоссияAzov-Black Sea Engineering Institute of FSBEI HE Don State Agrarian University (21 Lenin st., Zernograd, Russian Federation)Russian Federation2019280320233261Copyright © Сухинов А.И., Сидорякина В.В., Никитина А.В., Чистяков А.Е., Филина А.А., Литвинов В.Н., 20232023Сухинов А.И., Сидорякина В.В., Никитина А.В., Чистяков А.Е., Филина А.А., Литвинов В.Н.Sukhinov A.I., Sidoryakina V.V., Nikitina A.V., Chistyakov A.E., Filina A.A., Litvinov V.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.cmit-journal.ru/jour/article/view/61

Статья посвящена исследованию нелинейных эффектов в динамике популяций промысловой рыбы пеленгас Азовского моря в малых и больших размерах с учетом эффекта Аллее, конкуренции за ресурсы, отлова, пространственного распределения биогенного вещества и детрита на основе мультивидовой модели взаимодействия планктона и рыбы. Дискретный аналог разработанной модельной задачи водной экологии, входящий в программный комплекс, рассчитывался по схемам второго порядка точности с учетом частичного заполнения вычислительных ячеек. Система сеточных уравнений большой размерности, возникающих при дискретизации, была решена на основе двухслойного метода вариационного типа ‒ метода минимальных поправок, имеющего максимальную скорость сходимости. Разработаны эффективные параллельные алгоритмы для численной реализации задачи биологической кинетики, ориентированные на графический ускоритель NVIDIA Tesla K80 с модификацией формата хранения данных. В связи с этим процессы воспроизводства популяций биогеоценоза анализировались в реальном и ускоренном времени.

Paper covers the research of nonlinear effects in population dynamics of the pelengas commercial fish of the Azov Sea at low and high size taking into account the Allee effect, competition for resources, taxis, catching, spatial distribution of biogenic matter and detritus based on a multi-species model of plankton and fish interaction. Discrete analogue of developed model problem of water ecology, included in a software complex, were calculated using schemes of second order of accuracy taking into account the partial filling of computational cells. The system of grid equations of large dimension, arising at discretization, has been solved on the basis of a two-layer variational type method – the minimum corrections method having the maximum convergence rate. Effective parallel algorithms were developed for numerical implementation of biological kinetics problem and oriented on NVIDIA Tesla K80 graphics accelerator with the data storage format modification. Due to it, the reproduction processes of biogeocenose populations have been analyzed in real and accelerated time.

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The authors declare that there are no conflicts of interest present.