Stochastic sensitivity analysis of dynamic transformations in the “two prey – predator” model
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Stochastic sensitivity analysis of dynamic transformations in the “two prey – predator” model
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| Автор |
Bashkirtseva, I. A.
Perevalova, T. V. Ryashko, L. B. |
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| Тематика |
BIFURCATIONS
BIRHYTHMICITY CHAOS CONFIDENCE REGIONS EQUILIBRIA OSCILLATIONS POPULATION DYNAMICS RANDOM PERTURBATIONS STOCHASTIC SENSITIVITY “TWO PREY – PREDATOR” MODEL |
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| Описание |
This work is devoted to the study of the problem of modeling and analyzing complex oscillatory modes, both regular and chaotic, in systems of interacting populations in the presence of random perturbations. As an initial conceptual deterministic model, a Volterra system of three differential equations is considered, which describes the dynamics of prey populations of two competing species and a predator. This model takes into account the following key biological factors: the natural increase in prey, their intraspecific and interspecific competition, the extinction of predators in the absence of prey, the rate of predation by predators, the growth of the predator population due to predation, and the intensity of intraspecific competition in the predator population. The growth rate of the second prey population is used as a bifurcation parameter. At a certain interval of variation of this parameter, the system demonstrates a wide variety of dynamic modes: equilibrium, oscillatory, and chaotic. An important feature of this model is multistability. In this paper, we focus on the study of the parametric zone of tristability, when a stable equilibrium and two limit cycles coexist in the system. Such birhythmicity in the presence of random perturbations generates new dynamic modes that have no analogues in the deterministic case. The aim of the paper is a detailed study of stochastic phenomena caused by random fluctuations in the growth rate of the second population of prey. As a mathematical model of such fluctuations, we consider white Gaussian noise. Using methods of direct numerical modeling of solutions of the corresponding system of stochastic differential equations, the following phenomena have been identified and described: unidirectional stochastic transitions from one cycle to another, trigger mode caused by transitions between cycles, noise-induced transitions from cycles to the equilibrium, corresponding to the extinction of the predator and the second prey population. The paper presents the results of the analysis of these phenomena using the Lyapunov exponents, and identifies the parametric conditions for transitions from order to chaos and from chaos to order. For the analytical study of such noise-induced multi-stage transitions, the technique of stochastic sensitivity functions and the method of confidence regions were applied. The paper shows how this mathematical apparatus allows predicting the intensity of noise, leading to qualitative transformations of the modes of stochastic population dynamics. © 2022 Irina A. Bashkirtseva, Tatyana V. Perevalova, Lev B. Ryashko.
Russian Science Foundation, RSF, (21-11-00062) This work was supported Russian Science Foundation (No. 21-11-00062). |
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| Дата |
2024-04-08T11:08:03Z
2024-04-08T11:08:03Z 2022 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Башкирцева, ИА, Перевалова, ТВ & Ряшко, ЛБ 2022, 'МЕТОД СТОХАСТИЧЕСКОЙ ЧУВСТВИТЕЛЬНОСТИ В АНАЛИЗЕ ДИНАМИЧЕСКИХ ТРАНСФОРМАЦИЙ В МОДЕЛИ «ДВЕ ЖЕРТВЫ - ХИЩНИК»', Компьютерные исследования и моделирование, Том. 14, № 6, стр. 1343-1356. https://doi.org/10.20537/2076-7633-2022-14-6-1343-1356
Башкирцева, И. А., Перевалова, Т. В., & Ряшко, Л. Б. (2022). МЕТОД СТОХАСТИЧЕСКОЙ ЧУВСТВИТЕЛЬНОСТИ В АНАЛИЗЕ ДИНАМИЧЕСКИХ ТРАНСФОРМАЦИЙ В МОДЕЛИ «ДВЕ ЖЕРТВЫ - ХИЩНИК». Компьютерные исследования и моделирование, 14(6), 1343-1356. https://doi.org/10.20537/2076-7633-2022-14-6-1343-1356 2076-7633 Final All Open Access; Gold Open Access http://crm.ics.org.ru/uploads/crmissues/crm_2022_06/43_bashkirtseva.pdf http://crm.ics.org.ru/uploads/crmissues/crm_2022_06/43_bashkirtseva.pdf http://elar.urfu.ru/handle/10995/131565 50053149 10.20537/2076-7633-2022-14-6-1343-1356 85148633882 |
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| Язык |
ru
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| Связанные ресурсы |
info:eu-repo/grantAgreement/RSF//21-11-00062
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| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by-nd https://creativecommons.org/licenses/by-nd/4.0/ |
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| Формат |
application/pdf
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| Издатель |
Institute of Computer Science Izhevsk
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| Источник |
Computer Research and Modeling
Computer Research and Modeling |
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