About Bifurcations at Small Perturbations in a Logistic Equation with Delay
The article considers bifurcation problems for a logistic equation with delay at small perturbations. The most interesting results are for the case when small perturbations contain a large delay. The main results are special nonlinear equations of evolution in the normal form. Their nonlocal dynamic...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Yaroslavl State University
2017-04-01
|
| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/507 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1839573300258275328 |
|---|---|
| author | Sergey A. Kashchenko |
| author_facet | Sergey A. Kashchenko |
| author_sort | Sergey A. Kashchenko |
| collection | DOAJ |
| description | The article considers bifurcation problems for a logistic equation with delay at small perturbations. The most interesting results are for the case when small perturbations contain a large delay. The main results are special nonlinear equations of evolution in the normal form. Their nonlocal dynamics defines the behaviour of the solutions of the original equation in a small neigbourhood of the balance state or the cycle. It turns out that the order of large delay magnitude is principal. For the simplest case, when this order is congruent with the magnitude inverse to the small parameter appearing in the equation, the normal form is a complex equation with delay. In the case when the order of the delay coefficient is even higher, the normal form is presented by a multiparameter family of special boundary-value problems of degenerate-parabolic type. All these things allow to make a conclusion about the fact that in the considered problems with large delay the multistability is typical. |
| format | Article |
| id | doaj-art-1ccaf409088f43f6acff415ecd0f91a2 |
| institution | Matheson Library |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2017-04-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-1ccaf409088f43f6acff415ecd0f91a22025-08-04T14:06:37ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172017-04-0124216818510.18255/1818-1015-2017-2-168-185360About Bifurcations at Small Perturbations in a Logistic Equation with DelaySergey A. Kashchenko0P.G. Demidov Yaroslavl State UniversityThe article considers bifurcation problems for a logistic equation with delay at small perturbations. The most interesting results are for the case when small perturbations contain a large delay. The main results are special nonlinear equations of evolution in the normal form. Their nonlocal dynamics defines the behaviour of the solutions of the original equation in a small neigbourhood of the balance state or the cycle. It turns out that the order of large delay magnitude is principal. For the simplest case, when this order is congruent with the magnitude inverse to the small parameter appearing in the equation, the normal form is a complex equation with delay. In the case when the order of the delay coefficient is even higher, the normal form is presented by a multiparameter family of special boundary-value problems of degenerate-parabolic type. All these things allow to make a conclusion about the fact that in the considered problems with large delay the multistability is typical.https://www.mais-journal.ru/jour/article/view/507nonlinear dynamicsbifurcationasymptotic presentation |
| spellingShingle | Sergey A. Kashchenko About Bifurcations at Small Perturbations in a Logistic Equation with Delay Моделирование и анализ информационных систем nonlinear dynamics bifurcation asymptotic presentation |
| title | About Bifurcations at Small Perturbations in a Logistic Equation with Delay |
| title_full | About Bifurcations at Small Perturbations in a Logistic Equation with Delay |
| title_fullStr | About Bifurcations at Small Perturbations in a Logistic Equation with Delay |
| title_full_unstemmed | About Bifurcations at Small Perturbations in a Logistic Equation with Delay |
| title_short | About Bifurcations at Small Perturbations in a Logistic Equation with Delay |
| title_sort | about bifurcations at small perturbations in a logistic equation with delay |
| topic | nonlinear dynamics bifurcation asymptotic presentation |
| url | https://www.mais-journal.ru/jour/article/view/507 |
| work_keys_str_mv | AT sergeyakashchenko aboutbifurcationsatsmallperturbationsinalogisticequationwithdelay |