Influence of the Environment on Pattern Formation in the One-Dimensional Nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov Model

A. V. Shapovalov, V. V. Obukhov

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A self-consistent model of the dynamics of a cellular population described by the generalized Fisher–Kolmogorov–Petrovskii–Piskunov equation with nonlocal competitive losses and interaction with the environment is formulated, in which the dynamics is described by the diffusion equation with allowance for the interaction of the population and the environment. With the help of computer modeling, the formation of the population pattern under the influence of the environment is considered. Possible applications of the model and its generalizations are discussed.

Original languageEnglish
Pages (from-to)1093-1099
Number of pages7
JournalRussian Physics Journal
Volume61
Issue number6
DOIs
Publication statusPublished - 1 Oct 2018

Fingerprint

allowances
interactions

Keywords

  • nonlocal generalized Fisher–Kolmogorov–Petrovskii–Piskunov equation
  • pattern formation
  • selfconsistent model

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Influence of the Environment on Pattern Formation in the One-Dimensional Nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov Model. / Shapovalov, A. V.; Obukhov, V. V.

In: Russian Physics Journal, Vol. 61, No. 6, 01.10.2018, p. 1093-1099.

Research output: Contribution to journalArticle

@article{1d8d8a60490b40b1ab1dc2e78f7eb8f4,
title = "Influence of the Environment on Pattern Formation in the One-Dimensional Nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov Model",
abstract = "A self-consistent model of the dynamics of a cellular population described by the generalized Fisher–Kolmogorov–Petrovskii–Piskunov equation with nonlocal competitive losses and interaction with the environment is formulated, in which the dynamics is described by the diffusion equation with allowance for the interaction of the population and the environment. With the help of computer modeling, the formation of the population pattern under the influence of the environment is considered. Possible applications of the model and its generalizations are discussed.",
keywords = "nonlocal generalized Fisher–Kolmogorov–Petrovskii–Piskunov equation, pattern formation, selfconsistent model",
author = "Shapovalov, {A. V.} and Obukhov, {V. V.}",
year = "2018",
month = "10",
day = "1",
doi = "10.1007/s11182-018-1501-8",
language = "English",
volume = "61",
pages = "1093--1099",
journal = "Russian Physics Journal",
issn = "1064-8887",
publisher = "Consultants Bureau",
number = "6",

}

TY - JOUR

T1 - Influence of the Environment on Pattern Formation in the One-Dimensional Nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov Model

AU - Shapovalov, A. V.

AU - Obukhov, V. V.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - A self-consistent model of the dynamics of a cellular population described by the generalized Fisher–Kolmogorov–Petrovskii–Piskunov equation with nonlocal competitive losses and interaction with the environment is formulated, in which the dynamics is described by the diffusion equation with allowance for the interaction of the population and the environment. With the help of computer modeling, the formation of the population pattern under the influence of the environment is considered. Possible applications of the model and its generalizations are discussed.

AB - A self-consistent model of the dynamics of a cellular population described by the generalized Fisher–Kolmogorov–Petrovskii–Piskunov equation with nonlocal competitive losses and interaction with the environment is formulated, in which the dynamics is described by the diffusion equation with allowance for the interaction of the population and the environment. With the help of computer modeling, the formation of the population pattern under the influence of the environment is considered. Possible applications of the model and its generalizations are discussed.

KW - nonlocal generalized Fisher–Kolmogorov–Petrovskii–Piskunov equation

KW - pattern formation

KW - selfconsistent model

UR - http://www.scopus.com/inward/record.url?scp=85055122648&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055122648&partnerID=8YFLogxK

U2 - 10.1007/s11182-018-1501-8

DO - 10.1007/s11182-018-1501-8

M3 - Article

AN - SCOPUS:85055122648

VL - 61

SP - 1093

EP - 1099

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 6

ER -