Approximate solutions and symmetry of a two-component nonlocal reaction-diffusion population model of the Fisher-KPP type
We propose an approximate analytical approach to a (1+1) dimensional two-component system consisting of a nonlocal generalization of the well-known Fisher-Kolmogorov-Petrovskii- Piskunov (KPP) population equation and a diffusion equation for the density of the active substance solution surrounding t...
| Published in: | Symmetry Vol. 11, № 3. P. 366 (1-19) |
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| Main Author: | |
| Other Authors: | |
| Format: | Article |
| Language: | English |
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| Online Access: | http://vital.lib.tsu.ru/vital/access/manager/Repository/vtls:000660104 Перейти в каталог НБ ТГУ |
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| 008 | 190704|2019 sz s a eng d | ||
| 024 | 7 | |a 10.3390/sym11030366 |2 doi | |
| 035 | |a to000660104 | ||
| 039 | 9 | |a 201907081554 |c 201907041629 |d VLOAD |y 201907041626 |z Александр Эльверович Гилязов | |
| 040 | |a RU-ToGU |b rus |c RU-ToGU | ||
| 100 | 1 | |a Shapovalov, Alexander V. |9 90375 | |
| 245 | 1 | 0 | |a Approximate solutions and symmetry of a two-component nonlocal reaction-diffusion population model of the Fisher-KPP type |c A. V. Shapovalov, A. Yu. Trifonov |
| 504 | |a Библиогр.: 39 назв. | ||
| 520 | 3 | |a We propose an approximate analytical approach to a (1+1) dimensional two-component system consisting of a nonlocal generalization of the well-known Fisher-Kolmogorov-Petrovskii- Piskunov (KPP) population equation and a diffusion equation for the density of the active substance solution surrounding the population. Both equations of the system have terms that describe the interaction effects between the population and the active substance. The first order perturbation theory is applied to the system assuming that the interaction parameter is small. The Wentzel-Kramers-Brillouin (WKB)-Maslov semiclassical approximation is applied to the generalized nonlocal Fisher-KPP equation with the diffusion parameter assumed to be small, which corresponds to population dynamics under certain conditions. In the framework of the approach proposed, we consider symmetry operators which can be used to construct families of special approximate solutions to the system of model equations, and the procedure for constructing the solutions is illustrated by an example. The approximate solutions are discussed in the context of the released activity effect variously debated in the literature. | |
| 653 | |a Фишера-Колмогорова-Петровского-Пискунова уравнение | ||
| 653 | |a приближенные решения | ||
| 653 | |a квазиклассическое приближение | ||
| 653 | |a симметрия | ||
| 655 | 4 | |a статьи в журналах |9 879358 | |
| 700 | 1 | |a Trifonov, Andrey Yu. |d 1963-2021 |9 94516 | |
| 773 | 0 | |t Symmetry |d 2019 |g Vol. 11, № 3. P. 366 (1-19) |x 2073-8994 | |
| 852 | 4 | |a RU-ToGU | |
| 856 | 4 | |u http://vital.lib.tsu.ru/vital/access/manager/Repository/vtls:000660104 | |
| 856 | |y Перейти в каталог НБ ТГУ |u https://koha.lib.tsu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=457437 | ||
| 908 | |a статья | ||
| 999 | |c 457437 |d 457437 | ||