This article is cited in 1 scientific paper (total in 1 paper)
Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion
S. A. Kaschenkoab, V. E. Frolovb
a P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia
b National Research Nuclear University MEPhI, Kashirskoye shosse, 31, Moscow, 115409, Russia
We study the dynamics of finite-difference approximation on spatial variables of a logistic equation with delay and diffusion. It is assumed that the diffusion coefficient is small and the Malthusian coefficient is large. The question of the existence and asymptotic behavior of attractors was studied with special asymptotic methods.
It is shown that there is a rich array of different types of attractors in the phase space: leading centers, spiral waves, etc. The main asymptotic characteristics of all solutions from the corresponding attractors are adduced in this work. Typical graphics of wave fronts motion of different structures are represented in the article.
logistic equation, attractor, guiding center, helicon waves, asymptotics, stability.
PDF file (627 kB)
S. A. Kaschenko, V. E. Frolov, “Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion”, Model. Anal. Inform. Sist., 21:1 (2014), 94–114
Citation in format AMSBIB
\by S.~A.~Kaschenko, V.~E.~Frolov
\paper Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion
\jour Model. Anal. Inform. Sist.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “A self-symmetric cycle in a system of two diffusely connected Hutchinson's equations”, Sb. Math., 210:2 (2019), 184–233
|Number of views:|