Spatially inhomogeneous structures in the solution of Fisher-Kolmogorov equation with delay

International Conference on Computer Simulation in Physics and Beyond 2015

物理学;计算机科学

Aleshin, S.V.^1,2 ; Glyzin, S.D.^1,2 ; Kaschenko, S.A.^1,3

P.G. Demidov Yaroslavl State University, Sovetskaya str. 14, Yaroslavl

150000, Russia^1

Scientific Center in Chernogolovka RAS, Lesnaya str. 9, Chernogolovka, Moscow region

142432, Russia^2

National Research Nuclear University MEPhI, Kashirskoye shosse 31, Moscow

115409, Russia^3

关键词: Fisher-Kolmogorov equations;    Ginzburg-Landau equations;    Initial perturbation;    Oscillatory components;    Periodic boundary conditions;    Qualitative behavior;    Spatially inhomogeneous structures;    Spatio-temporal fluctuations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/681/1/012023/pdf
DOI  :  10.1088/1742-6596/681/1/012023

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

We consider the problem of density wave propagation in a logistic equation with delay and diffusion (Fisher-Kolmogorov equation with delay). A Ginzburg-Landau equation was constructed in order to study the qualitative behavior of the solution near the equilibrium state. The numerical analysis of wave propagation shows that for a sufficiently small delay this equation has a solution similar to the solution of a classical Fisher-Kolmogorov equation. The delay increasing leads to existence of the oscillatory component in spatial distribution of solutions. A further increase of delay leads to destruction of the traveling wave. That is expressed in the fact that undamped spatio-temporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the delay is sufficiently large we observe intensive spatio-temporal fluctuations in the whole area of wave propagation.