Dynamics analysis of Mackey-Glass model with two variable delays
Dynamics of non-autonomous Mackey-Glass model have not been well documented yet in two variable delays case, which is proposed by Berezansky and Braverman as open problems. This manuscript considers attractivity of all non-oscillating solutions about the positive equilibrium point and the global asy...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-06-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2020249?viewType=HTML |
| _version_ | 1818692332278513664 |
|---|---|
| author | Yanxiang Tan |
| author_facet | Yanxiang Tan |
| author_sort | Yanxiang Tan |
| collection | DOAJ |
| description | Dynamics of non-autonomous Mackey-Glass model have not been well documented yet in two variable delays case, which is proposed by Berezansky and Braverman as open problems. This manuscript considers attractivity of all non-oscillating solutions about the positive equilibrium point and the global asymptotical stability of the trivial equilibrium point. Two delay-independent criteria based on the fluctuation lemma and techniques of differential inequality are established. The obtained results improve and complement some published results. Meanwhile, computer simulations of two numerical examples are arranged to illustrate the correctness and effectiveness of the presented results. |
| first_indexed | 2024-12-17T12:56:06Z |
| format | Article |
| id | doaj.art-ef541cbe3f9b43e08f007ede58a5f392 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-17T12:56:06Z |
| publishDate | 2020-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-ef541cbe3f9b43e08f007ede58a5f3922022-12-21T21:47:29ZengAIMS PressMathematical Biosciences and Engineering1551-00182020-06-011754513452610.3934/mbe.2020249Dynamics analysis of Mackey-Glass model with two variable delaysYanxiang Tan 0School of Mathematics and Statistics, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, ChinaDynamics of non-autonomous Mackey-Glass model have not been well documented yet in two variable delays case, which is proposed by Berezansky and Braverman as open problems. This manuscript considers attractivity of all non-oscillating solutions about the positive equilibrium point and the global asymptotical stability of the trivial equilibrium point. Two delay-independent criteria based on the fluctuation lemma and techniques of differential inequality are established. The obtained results improve and complement some published results. Meanwhile, computer simulations of two numerical examples are arranged to illustrate the correctness and effectiveness of the presented results.https://www.aimspress.com/article/doi/10.3934/mbe.2020249?viewType=HTMLmackey-glass modeldelayglobal attractivitystability |
| spellingShingle | Yanxiang Tan Dynamics analysis of Mackey-Glass model with two variable delays Mathematical Biosciences and Engineering mackey-glass model delay global attractivity stability |
| title | Dynamics analysis of Mackey-Glass model with two variable delays |
| title_full | Dynamics analysis of Mackey-Glass model with two variable delays |
| title_fullStr | Dynamics analysis of Mackey-Glass model with two variable delays |
| title_full_unstemmed | Dynamics analysis of Mackey-Glass model with two variable delays |
| title_short | Dynamics analysis of Mackey-Glass model with two variable delays |
| title_sort | dynamics analysis of mackey glass model with two variable delays |
| topic | mackey-glass model delay global attractivity stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2020249?viewType=HTML |
| work_keys_str_mv | AT yanxiangtan dynamicsanalysisofmackeyglassmodelwithtwovariabledelays |