Global Stability for a Semidiscrete Logistic System with Feedback Control

Global Stability for a Semidiscrete Logistic System with Feedback Control

In this paper, a semidiscrete logistic model with the Dirichlet boundary conditions and feedback controls is proposed. By means of the sub- and supper-solution method and eigenvalue theory, the unique positive equilibrium is proved. By constructing a suitable Lyapunov function, the global asymptomat...

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Main Authors: Li Xu, Shanshan Lou, Ruiwen Han
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2020/3189515
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spelling doaj-df146cc9051c441eb1d241b3fcccf34c2020-11-25T03:31:56ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/31895153189515Global Stability for a Semidiscrete Logistic System with Feedback ControlLi Xu0Shanshan Lou1Ruiwen Han2School of Mathematics, Tianjin University, Tianjin 300072, ChinaSchool of Science, Tianjin University of Commerce, Tianjin 300134, ChinaSchool of Science, Tianjin University of Commerce, Tianjin 300134, ChinaIn this paper, a semidiscrete logistic model with the Dirichlet boundary conditions and feedback controls is proposed. By means of the sub- and supper-solution method and eigenvalue theory, the unique positive equilibrium is proved. By constructing a suitable Lyapunov function, the global asymptomatic stability of the unique positive equilibrium is investigated. Finally, numerical simulations are presented to verify the effectiveness of the main results.http://dx.doi.org/10.1155/2020/3189515
collection DOAJ
language English
format Article
sources DOAJ
author Li Xu
Shanshan Lou
Ruiwen Han
spellingShingle Li Xu
Shanshan Lou
Ruiwen Han
Global Stability for a Semidiscrete Logistic System with Feedback Control
Discrete Dynamics in Nature and Society
author_facet Li Xu
Shanshan Lou
Ruiwen Han
author_sort Li Xu
title Global Stability for a Semidiscrete Logistic System with Feedback Control
title_short Global Stability for a Semidiscrete Logistic System with Feedback Control
title_full Global Stability for a Semidiscrete Logistic System with Feedback Control
title_fullStr Global Stability for a Semidiscrete Logistic System with Feedback Control
title_full_unstemmed Global Stability for a Semidiscrete Logistic System with Feedback Control
title_sort global stability for a semidiscrete logistic system with feedback control
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2020-01-01
description In this paper, a semidiscrete logistic model with the Dirichlet boundary conditions and feedback controls is proposed. By means of the sub- and supper-solution method and eigenvalue theory, the unique positive equilibrium is proved. By constructing a suitable Lyapunov function, the global asymptomatic stability of the unique positive equilibrium is investigated. Finally, numerical simulations are presented to verify the effectiveness of the main results.
url http://dx.doi.org/10.1155/2020/3189515
work_keys_str_mv AT lixu globalstabilityforasemidiscretelogisticsystemwithfeedbackcontrol
AT shanshanlou globalstabilityforasemidiscretelogisticsystemwithfeedbackcontrol
AT ruiwenhan globalstabilityforasemidiscretelogisticsystemwithfeedbackcontrol
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