A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Numerical modeling of population 2D-dynamics with nonlocal interaction”, Computer Research and Modeling, 2010, Volume 2, Issue 1,Pages <nobr>33

This article is cited in 4 papers

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Numerical modeling of population 2D-dynamics with nonlocal interaction

A. V. Borisov^a, A. Yu. Trifonov^b, A. V. Shapovalov^a

^a Tomsk State University, Lenin av., 36, Tomsk, Russia, 634050
^b National Research Tomsk Polytechnic University, Lenin av., 30, Tomsk, Russia, 634050

Abstract: Numerical solutions for the two-dimensional reaction-diffusion equation with nonlocal nonlinearity are obtained. The solutions reveal formation of dissipative structures. Structures arising from initial distributions with one and several centers of localization are considered. Formation of extending circular structures is shown. Peculiarities of formation and interaction of extending circular structures depending on nonlocal interaction are considered.

Keywords: reaction-diffusion systems, nonlocal interactions, circular pattern formation.

UDC: 577.3.01; 577.38

Received: 24.03.2010
Revised: 03.05.2010

DOI: 10.20537/2076-7633-2010-2-1-33-40