Approximate Solutions and Symmetry of a Two-Component Nonlocal Reaction-Diffusion Population Model of the Fisher-KPP Type; Symmetry; Vol. 11, iss. 3
| Parent link: | Symmetry Vol. 11, iss. 3.— 2019.— [366, 19 p.] |
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| Zusammenfassung: | Title screen 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. |
| Sprache: | Englisch |
| Veröffentlicht: |
2019
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| Schlagworte: | |
| Online-Zugang: | https://doi.org/10.3390/sym11030366 |
| Format: | Elektronisch Buchkapitel |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=665283 |
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| 200 | 1 | |a Approximate Solutions and Symmetry of a Two-Component Nonlocal Reaction-Diffusion Population Model of the Fisher-KPP Type |f A. V. Shapovalov, A. Yu. Trifonov | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: 39 tit.] | ||
| 330 | |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. | ||
| 461 | |t Symmetry | ||
| 463 | |t Vol. 11, iss. 3 |v [366, 19 p.] |d 2019 | ||
| 610 | 1 | |a электронный ресурс | |
| 610 | 1 | |a труды учёных ТПУ | |
| 610 | 1 | |a nonlocal Fisher–KPP model | |
| 610 | 1 | |a reaction-diffusion | |
| 610 | 1 | |a semiclassical approximation | |
| 610 | 1 | |a perturbation method | |
| 610 | 1 | |a symmetries | |
| 610 | 1 | |a released activity | |
| 610 | 1 | |a модель Фишера | |
| 610 | 1 | |a диффузия | |
| 610 | 1 | |a возмущения | |
| 610 | 1 | |a симметрия | |
| 700 | 1 | |a Shapovalov |b A. V. |g Aleksandr Vasiljevich | |
| 701 | 1 | |a Trifonov |b A. Yu. |c physicist, mathematician |c Professor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences |f 1963- |g Andrey Yurievich |3 (RuTPU)RU\TPU\pers\30754 | |
| 712 | 0 | 2 | |a Национальный исследовательский Томский политехнический университет |b Школа базовой инженерной подготовки |b Отделение математики и информатики |3 (RuTPU)RU\TPU\col\23555 |
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| 856 | 4 | |u https://doi.org/10.3390/sym11030366 | |
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