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JOURNALS // Computer Research and Modeling // Archive

Computer Research and Modeling, 2011 Volume 3, Issue 1, Pages 55–61 (Mi crm547)

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Convection effect on two-dimensional dynamicsin the nonlocal reaction-diffusion model

A. V. Borisova, A. Yu. Trifonovb, A. V. Shapovalova

a Tomsk State University, 36 Lenin Prospekt, Tomsk, 634050, Russia
b Tomsk State Polytechnic University, 30 Lenin Prospekt, Tomsk, 634050, Russia

Abstract: Pattern formation described by the scalar Fisher–Kolmogorov–Petrovsky–Piscounov equation with nonlocal competition loses and convection linear on coordinates is considered numerically. Initial function localized around a point is shown to transform in a function localized around a ring with symmetrically sited local maxima. The ring radius and number of maxima depend on convection.

Keywords: reaction-diffusion, convection, nonlocal competition losses, Fisher–Kolmogorov–Petrovsky–Piscounov equation.

UDC: 519.8

Received: 10.02.2011

DOI: 10.20537/2076-7633-2011-3-1-55-61



© Steklov Math. Inst. of RAS, 2025