Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion
We study the dynamics of finite-difference approximation on spatial variables of a logistic equation with delay and diffusion. It is assumed that the diffusion coefficient is small and the Malthusian coefficient is large. The question of the existence and asymptotic behavior of attractors was studie...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2014-02-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/131 |
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| author | S. A. Kaschenko V. E. Frolov |
| author_facet | S. A. Kaschenko V. E. Frolov |
| author_sort | S. A. Kaschenko |
| collection | DOAJ |
| description | We study the dynamics of finite-difference approximation on spatial variables of a logistic equation with delay and diffusion. It is assumed that the diffusion coefficient is small and the Malthusian coefficient is large. The question of the existence and asymptotic behavior of attractors was studied with special asymptotic methods. It is shown that there is a rich array of different types of attractors in the phase space: leading centers, spiral waves, etc. The main asymptotic characteristics of all solutions from the corresponding attractors are adduced in this work. Typical graphics of wave fronts motion of different structures are represented in the article. |
| format | Article |
| id | doaj-art-5bf6cf1e381c4dd3824612bd612e71ae |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2014-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-5bf6cf1e381c4dd3824612bd612e71ae2025-08-20T03:44:18ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172014-02-012119411410.18255/1818-1015-2014-1-94-114125Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small DiffusionS. A. Kaschenko0V. E. Frolov1P.G. Demidov Yaroslavl State University; National Research Nuclear University MEPhINational Research Nuclear University MEPhIWe study the dynamics of finite-difference approximation on spatial variables of a logistic equation with delay and diffusion. It is assumed that the diffusion coefficient is small and the Malthusian coefficient is large. The question of the existence and asymptotic behavior of attractors was studied with special asymptotic methods. It is shown that there is a rich array of different types of attractors in the phase space: leading centers, spiral waves, etc. The main asymptotic characteristics of all solutions from the corresponding attractors are adduced in this work. Typical graphics of wave fronts motion of different structures are represented in the article.https://www.mais-journal.ru/jour/article/view/131logistic equationattractorguiding centerhelicon wavesasymptoticsstability |
| spellingShingle | S. A. Kaschenko V. E. Frolov Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion Моделирование и анализ информационных систем logistic equation attractor guiding center helicon waves asymptotics stability |
| title | Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion |
| title_full | Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion |
| title_fullStr | Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion |
| title_full_unstemmed | Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion |
| title_short | Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion |
| title_sort | asymptotics of a steady state condition of finite difference approximation of a logistic equation with delay and small diffusion |
| topic | logistic equation attractor guiding center helicon waves asymptotics stability |
| url | https://www.mais-journal.ru/jour/article/view/131 |
| work_keys_str_mv | AT sakaschenko asymptoticsofasteadystateconditionoffinitedifferenceapproximationofalogisticequationwithdelayandsmalldiffusion AT vefrolov asymptoticsofasteadystateconditionoffinitedifferenceapproximationofalogisticequationwithdelayandsmalldiffusion |