Local Dynamics of a Logistic Equation with Delay
We considered a logistic equation with delay and studied its local dynamics. The critical cases have been found in the problem of the equilibrium state stability. We applied standard Andronov-Hopf biffurcation methods for delay differential equations and an asymptotic method, developed by one of the...
| Main Authors: | , |
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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 |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/129 |
| _version_ | 1826559001605701632 |
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| author | S. V. Aleshin S. A. Kaschenko |
| author_facet | S. V. Aleshin S. A. Kaschenko |
| author_sort | S. V. Aleshin |
| collection | DOAJ |
| description | We considered a logistic equation with delay and studied its local dynamics. The critical cases have been found in the problem of the equilibrium state stability. We applied standard Andronov-Hopf biffurcation methods for delay differential equations and an asymptotic method, developed by one of the authors, based on the construction of special evolution equations that define the local dynamics equations with delay. It is shown that all solutions of the equation tend to an equilibrium state or result in a single stable cycle. The results of numerical modelling are presented in this paper. The study has proved that analytical and numerical modeling results have a good correlation. |
| first_indexed | 2024-04-10T02:25:31Z |
| format | Article |
| id | doaj.art-f27dcb08724f4eb59c1f115122fab6ce |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2025-03-14T08:53:27Z |
| publishDate | 2014-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-f27dcb08724f4eb59c1f115122fab6ce2025-03-02T12:46:55ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172014-02-01211738810.18255/1818-1015-2014-1-73-88123Local Dynamics of a Logistic Equation with DelayS. V. Aleshin0S. A. Kaschenko1P.G. Demidov Yaroslavl State UniversityP.G. Demidov Yaroslavl State UniversityWe considered a logistic equation with delay and studied its local dynamics. The critical cases have been found in the problem of the equilibrium state stability. We applied standard Andronov-Hopf biffurcation methods for delay differential equations and an asymptotic method, developed by one of the authors, based on the construction of special evolution equations that define the local dynamics equations with delay. It is shown that all solutions of the equation tend to an equilibrium state or result in a single stable cycle. The results of numerical modelling are presented in this paper. The study has proved that analytical and numerical modeling results have a good correlation.https://www.mais-journal.ru/jour/article/view/129logistic equationrelaxation cyclenormal fornequilibrium state |
| spellingShingle | S. V. Aleshin S. A. Kaschenko Local Dynamics of a Logistic Equation with Delay Моделирование и анализ информационных систем logistic equation relaxation cycle normal forn equilibrium state |
| title | Local Dynamics of a Logistic Equation with Delay |
| title_full | Local Dynamics of a Logistic Equation with Delay |
| title_fullStr | Local Dynamics of a Logistic Equation with Delay |
| title_full_unstemmed | Local Dynamics of a Logistic Equation with Delay |
| title_short | Local Dynamics of a Logistic Equation with Delay |
| title_sort | local dynamics of a logistic equation with delay |
| topic | logistic equation relaxation cycle normal forn equilibrium state |
| url | https://www.mais-journal.ru/jour/article/view/129 |
| work_keys_str_mv | AT svaleshin localdynamicsofalogisticequationwithdelay AT sakaschenko localdynamicsofalogisticequationwithdelay |