Fisher–Kolmogorov–Petrovskii–Piscounov Equation with Delay
We considered the problem of density wave propagation in a logistic equation with delay and diffusion (Fisher–Kolmogorov equation with delay). It was constructed a Ginzburg–Landau equation in order to study the qualitative behavior of the solution near the equilibrium state. The numerical analysis o...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2015-04-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/248 |
| _version_ | 1826558964273250304 |
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| author | S. V. Aleshin S. D. Glyzin S. A. Kaschenko |
| author_facet | S. V. Aleshin S. D. Glyzin S. A. Kaschenko |
| author_sort | S. V. Aleshin |
| collection | DOAJ |
| description | We considered the problem of density wave propagation in a logistic equation with delay and diffusion (Fisher–Kolmogorov equation with delay). It was constructed a Ginzburg–Landau equation in order to study the qualitative behavior of the solution near the equilibrium state. The numerical analysis of wave propagation shows that for a sufficiently small delay this equation has a solution similar to the solution of a classical Fisher–Kolmogorov equation. The delay increasing leads to existence of the oscillatory component in spatial distribution of solutions. A further increase of delay leads to the destruction of the traveling wave. That is expressed in the fact that undamped spatio-temporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the delay is sufficiently large we observe intensive spatio-temporal fluctuations in the whole area of wave propagation. |
| first_indexed | 2024-04-10T02:24:48Z |
| format | Article |
| id | doaj.art-540ebe72302d4ef6bfe19cb7ae501789 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2025-03-14T08:52:51Z |
| publishDate | 2015-04-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-540ebe72302d4ef6bfe19cb7ae5017892025-03-02T12:46:57ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-04-0122230432110.18255/1818-1015-2015-2-304-321241Fisher–Kolmogorov–Petrovskii–Piscounov Equation with DelayS. V. Aleshin0S. D. Glyzin1S. A. Kaschenko2P.G. Demidov Yaroslavl State University; Scientific Center in Chernogolovka RASP.G. Demidov Yaroslavl State University; Scientific Center in Chernogolovka RASP.G. Demidov Yaroslavl State University; National Research Nuclear University MEPhIWe considered the problem of density wave propagation in a logistic equation with delay and diffusion (Fisher–Kolmogorov equation with delay). It was constructed a Ginzburg–Landau equation in order to study the qualitative behavior of the solution near the equilibrium state. The numerical analysis of wave propagation shows that for a sufficiently small delay this equation has a solution similar to the solution of a classical Fisher–Kolmogorov equation. The delay increasing leads to existence of the oscillatory component in spatial distribution of solutions. A further increase of delay leads to the destruction of the traveling wave. That is expressed in the fact that undamped spatio-temporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the delay is sufficiently large we observe intensive spatio-temporal fluctuations in the whole area of wave propagation.https://www.mais-journal.ru/jour/article/view/248attractorbifurcationfisher–kolmogorov equationginzburg–landau equation |
| spellingShingle | S. V. Aleshin S. D. Glyzin S. A. Kaschenko Fisher–Kolmogorov–Petrovskii–Piscounov Equation with Delay Моделирование и анализ информационных систем attractor bifurcation fisher–kolmogorov equation ginzburg–landau equation |
| title | Fisher–Kolmogorov–Petrovskii–Piscounov Equation with Delay |
| title_full | Fisher–Kolmogorov–Petrovskii–Piscounov Equation with Delay |
| title_fullStr | Fisher–Kolmogorov–Petrovskii–Piscounov Equation with Delay |
| title_full_unstemmed | Fisher–Kolmogorov–Petrovskii–Piscounov Equation with Delay |
| title_short | Fisher–Kolmogorov–Petrovskii–Piscounov Equation with Delay |
| title_sort | fisher kolmogorov petrovskii piscounov equation with delay |
| topic | attractor bifurcation fisher–kolmogorov equation ginzburg–landau equation |
| url | https://www.mais-journal.ru/jour/article/view/248 |
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