Discrete-continuous model for the problem of analysis critical level of exploitation of bioresources
- Authors: Perevaryukha A.Y.1
-
Affiliations:
- St. Petersburg Institute for Informatics and Automation of RAS
- Issue: Vol 18, No 1 (2014)
- Pages: 145-155
- Section: Articles
- URL: https://ogarev-online.ru/1991-8615/article/view/20740
- DOI: https://doi.org/10.14498/vsgtu1116
- ID: 20740
Cite item
Full Text
Abstract
The article deals with the model developed in the framework of the research on the problem of replenishment of fish populations. A new approach takes into account the peculiarities of describing the changes in the number of generations by the system of ordinary differential equations. The method of models implementation in computing environment enables the simulation of various types of human impact, including the case of introduction of the new species to the environment. The author analyzes the behavior of scenarios of a population model with different levels of fishing impact and concludes the most dangerous case for the systematic management of bioresources. Examples and compared data on the dynamics of some commercial fish populations of the Volga basin are discussed. It is noted that a dangerous scenario for managing the bioresources is realized with continued slight excess of quotas.
Full Text
##article.viewOnOriginalSite##About the authors
Andrey Yu Perevaryukha
St. Petersburg Institute for Informatics and Automation of RAS
Email: madelf@pisem.net
(Cand. Technical (Computer) Sci.), Senior Researcher, Lab. of Applied Informatics 39, 14-ya liniya V. O., St. Petersburg, 199178, Russian Federation
References
- R. M. May, “Simple mathematical models with very complicated dynamics”, Nature, 1976, vol. 261, pp. 459-467. doi: 10.1038/261459a0.
- W. E. Ricker, “Stock and Recruitment”, J. Fish. Res. Bd. Canada, 1954, vol. 11, no. 5, pp. 559-623. doi: 10.1139/f54-039.
- А. Ю. Переварюха, “Анализ опыта моделирования биоресурсов с точки зрения современной теории динамических систем” // Экологические системы и приборы, 2011. No 11. С. 17-21.
- Д. М. Гробман, “Гомеоморфизм систем дифференциальных уравнений” // ДАН СССР, 1959. Т. 128, No 5. С. 880-881.
- Ph. Hartman, “On the local linearization of differential equations”, Proc. Amer. Math. Soc., 1963, vol. 14, no. 4, pp. 568-573. doi: 10.1090/s0002-9939-1963-0152718-3.
- M. J. Feigenbaum, “Universal behavior in nonlinear systems”, Physica D: Nonlinear Phenomena, 1983, vol. 7, no. 1-3, pp. 16-39. doi: 10.1016/0167-2789(83)90112-4.
- D. Singer, “Stable Orbits and Bifurcation of Maps of the Interval”, SIAM J. Appl. Math., 1978, vol. 35, no. 2, pp. 206-267. doi: 10.1137/0135020.
- А. Н. Шарковский, “Сосуществование циклов непрерывного преобразования прямой в себя” // Укр. мат. ж., 1964. Т. 16, No 1. С. 61-71.
- А. Н. Шарковский, С. Ф. Коляда, А. Г. Сивак, В. В. Федоренко, Динамика одномерных отображений, Киев: Наукова думка, 1989. 216 с.
- M. P. Shepard, F. C. Withler, “Spawning Stock Size and Resultant Production for Skeena Sockeye”, J. Fish. Res. Bd. Canada, 1958, vol. 15, no. 5, pp. 1007-1025. doi: 10.1139/f58-055.
- W. C. Allee, Edith S. Bowen, “Studies in animal aggregations: Mass protection against colloidal silver among goldfishes”, Journal of Experimental Zoology, 1932, vol. 61, no. 2, pp. 185-207. doi: 10.1002/jez.1400610202.
- П. В. Вещев, Г. И. Гутенева, “Эффективность естественного воспроизводства осетровых в низовьях Волги в современных условиях” // Экология, 2012. No 2. С. 123-128.
- А. П. Сливка, А. В. Павлов, “Биологические основы изменения режима промысла осетровых (Acipenseridae) в дельте Волги” // Вопросы ихтиологии, 1982. No 5. С. 738-745.
- Д. И. Постнов, А. Е. Минин, А. А. Клевакин, “Динамика рыбных запасов и возможности их освоения на Горьковском и Чебоксарском водохранилище” // Рыбное хозяйство, 2012. No 1. С. 60-62.
Supplementary files

