Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion

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 studie...

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Main Authors: S. A. Kaschenko, V. E. Frolov
Format: Article
Language:English
Published: Yaroslavl State University 2014-02-01
Series:Моделирование и анализ информационных систем
Subjects:
Online Access:https://www.mais-journal.ru/jour/article/view/131
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author S. A. Kaschenko
V. E. Frolov
author_facet S. A. Kaschenko
V. E. Frolov
author_sort S. A. Kaschenko
collection DOAJ
description 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.
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series Моделирование и анализ информационных систем
spelling doaj-art-5bf6cf1e381c4dd3824612bd612e71ae2025-08-20T03:44:18ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172014-02-012119411410.18255/1818-1015-2014-1-94-114125Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small DiffusionS. A. Kaschenko0V. E. Frolov1P.G. Demidov Yaroslavl State University; National Research Nuclear University MEPhINational Research Nuclear University MEPhIWe 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.https://www.mais-journal.ru/jour/article/view/131logistic equationattractorguiding centerhelicon wavesasymptoticsstability
spellingShingle 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
Моделирование и анализ информационных систем
logistic equation
attractor
guiding center
helicon waves
asymptotics
stability
title Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion
title_full Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion
title_fullStr Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion
title_full_unstemmed Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion
title_short Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion
title_sort asymptotics of a steady state condition of finite difference approximation of a logistic equation with delay and small diffusion
topic logistic equation
attractor
guiding center
helicon waves
asymptotics
stability
url https://www.mais-journal.ru/jour/article/view/131
work_keys_str_mv AT sakaschenko asymptoticsofasteadystateconditionoffinitedifferenceapproximationofalogisticequationwithdelayandsmalldiffusion
AT vefrolov asymptoticsofasteadystateconditionoffinitedifferenceapproximationofalogisticequationwithdelayandsmalldiffusion