Calculating Lyapunov Value for the Logistic Equation with Rapidly Oscillating Delay
We consider the local dynamic of the logistic equation with rapidly oscillating timeperiodic piecewise constant or piecewise linear coefficient of delay. It was shown that the averaged equation is a logistic equation with two delays in first case and logistic equation with distributed delay in secon...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2014-06-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/114 |
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| author | N. D. Bykova |
| author_facet | N. D. Bykova |
| author_sort | N. D. Bykova |
| collection | DOAJ |
| description | We consider the local dynamic of the logistic equation with rapidly oscillating timeperiodic piecewise constant or piecewise linear coefficient of delay. It was shown that the averaged equation is a logistic equation with two delays in first case and logistic equation with distributed delay in second case. The criterion of equilibrium point stability was obtained in both cases. Dynamical properties of the original equation were considered in the critical case of equilibrium point of averaged equation stability problem. It was shown, that local dynamic in the critical case is defined by Lyapunov value whose sign depends on the parameters of the problem. |
| format | Article |
| id | doaj-art-b6533dcad4ae4365b81e52a1685efbd3 |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2014-06-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-b6533dcad4ae4365b81e52a1685efbd32025-08-20T03:44:18ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172014-06-0121312112810.18255/1818-1015-2014-3-121-128108Calculating Lyapunov Value for the Logistic Equation with Rapidly Oscillating DelayN. D. Bykova0National Research Nuclear University MEPhI; P.G. Demidov Yaroslavl State UniversityWe consider the local dynamic of the logistic equation with rapidly oscillating timeperiodic piecewise constant or piecewise linear coefficient of delay. It was shown that the averaged equation is a logistic equation with two delays in first case and logistic equation with distributed delay in second case. The criterion of equilibrium point stability was obtained in both cases. Dynamical properties of the original equation were considered in the critical case of equilibrium point of averaged equation stability problem. It was shown, that local dynamic in the critical case is defined by Lyapunov value whose sign depends on the parameters of the problem.https://www.mais-journal.ru/jour/article/view/114averagingstabilitynonlinear dynamicsnormal form |
| spellingShingle | N. D. Bykova Calculating Lyapunov Value for the Logistic Equation with Rapidly Oscillating Delay Моделирование и анализ информационных систем averaging stability nonlinear dynamics normal form |
| title | Calculating Lyapunov Value for the Logistic Equation with Rapidly Oscillating Delay |
| title_full | Calculating Lyapunov Value for the Logistic Equation with Rapidly Oscillating Delay |
| title_fullStr | Calculating Lyapunov Value for the Logistic Equation with Rapidly Oscillating Delay |
| title_full_unstemmed | Calculating Lyapunov Value for the Logistic Equation with Rapidly Oscillating Delay |
| title_short | Calculating Lyapunov Value for the Logistic Equation with Rapidly Oscillating Delay |
| title_sort | calculating lyapunov value for the logistic equation with rapidly oscillating delay |
| topic | averaging stability nonlinear dynamics normal form |
| url | https://www.mais-journal.ru/jour/article/view/114 |
| work_keys_str_mv | AT ndbykova calculatinglyapunovvalueforthelogisticequationwithrapidlyoscillatingdelay |