Applying the Averaging Principle to a Logistic Equation with Rapidly Oscillating Delay
The problem about the local dynamics of the logistic equation with rapidly oscillating time-periodic piecewise constant coefficient of delay was considered. It was shown that the averaged equation is a logistic equation with two delays. The criterion of equilibrium point stability was obtained. Dyna...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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/130 |
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| Summary: | The problem about the local dynamics of the logistic equation with rapidly oscillating time-periodic piecewise constant coefficient of delay was considered. It was shown that the averaged equation is a logistic equation with two delays. The criterion of equilibrium point stability was obtained. Dynamical properties of the original equation was considered provided that the critical case of equilibrium point stability problem was implemented. It was found that an increase of delay coefficient oscillation frequency may lead to an unlimited process of “birth” and “death” steady mode. |
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| ISSN: | 1818-1015 2313-5417 |