Bifurcation and chaos in a discrete activator-inhibitor system
In this paper, we explore local dynamic characteristics, bifurcations and control in the discrete activator-inhibitor system. More specifically, it is proved that discrete-time activator-inhibitor system has an interior equilibrium solution. Then, by using linear stability theory, local dynamics wit...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023225?viewType=HTML |
| _version_ | 1797948303690694656 |
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| author | Abdul Qadeer Khan Zarqa Saleem Tarek Fawzi Ibrahim Khalid Osman Fatima Mushyih Alshehri Mohamed Abd El-Moneam |
| author_facet | Abdul Qadeer Khan Zarqa Saleem Tarek Fawzi Ibrahim Khalid Osman Fatima Mushyih Alshehri Mohamed Abd El-Moneam |
| author_sort | Abdul Qadeer Khan |
| collection | DOAJ |
| description | In this paper, we explore local dynamic characteristics, bifurcations and control in the discrete activator-inhibitor system. More specifically, it is proved that discrete-time activator-inhibitor system has an interior equilibrium solution. Then, by using linear stability theory, local dynamics with different topological classifications for the interior equilibrium solution are investigated. It is investigated that for the interior equilibrium solution, discrete activator-inhibitor system undergoes Neimark-Sacker and flip bifurcations. Further chaos control is studied by the feedback control method. Finally, numerical simulations are presented to validate the obtained theoretical results. |
| first_indexed | 2024-04-10T21:41:11Z |
| format | Article |
| id | doaj.art-2f441c79218e42b080a73566910a07ad |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T21:41:11Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-2f441c79218e42b080a73566910a07ad2023-01-19T01:23:30ZengAIMS PressAIMS Mathematics2473-69882023-01-01824551457410.3934/math.2023225Bifurcation and chaos in a discrete activator-inhibitor systemAbdul Qadeer Khan0Zarqa Saleem 1Tarek Fawzi Ibrahim2Khalid Osman3Fatima Mushyih Alshehri4Mohamed Abd El-Moneam 51. Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan1. Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan2. Department of Mathematics, Faculty of Sciences and Arts (Mahayel), King Khalid University Abha, Saudi Arabia 3. Department of Mathematics, Faculty of Science, Mansoura University, Egypt4. Department of Mathematics, Faculty of Sciences and Arts in Sarat Abeda, King Khalid University, Abha, Saudi Arabia5. Department of Mathematics, Faculty of Science, Jazan University, Saudi Arabia5. Department of Mathematics, Faculty of Science, Jazan University, Saudi ArabiaIn this paper, we explore local dynamic characteristics, bifurcations and control in the discrete activator-inhibitor system. More specifically, it is proved that discrete-time activator-inhibitor system has an interior equilibrium solution. Then, by using linear stability theory, local dynamics with different topological classifications for the interior equilibrium solution are investigated. It is investigated that for the interior equilibrium solution, discrete activator-inhibitor system undergoes Neimark-Sacker and flip bifurcations. Further chaos control is studied by the feedback control method. Finally, numerical simulations are presented to validate the obtained theoretical results.https://www.aimspress.com/article/doi/10.3934/math.2023225?viewType=HTMLactivator-inhibitor modelneimark-sacker bifurcationsflip bifurcationnumerical simulationchaos |
| spellingShingle | Abdul Qadeer Khan Zarqa Saleem Tarek Fawzi Ibrahim Khalid Osman Fatima Mushyih Alshehri Mohamed Abd El-Moneam Bifurcation and chaos in a discrete activator-inhibitor system AIMS Mathematics activator-inhibitor model neimark-sacker bifurcations flip bifurcation numerical simulation chaos |
| title | Bifurcation and chaos in a discrete activator-inhibitor system |
| title_full | Bifurcation and chaos in a discrete activator-inhibitor system |
| title_fullStr | Bifurcation and chaos in a discrete activator-inhibitor system |
| title_full_unstemmed | Bifurcation and chaos in a discrete activator-inhibitor system |
| title_short | Bifurcation and chaos in a discrete activator-inhibitor system |
| title_sort | bifurcation and chaos in a discrete activator inhibitor system |
| topic | activator-inhibitor model neimark-sacker bifurcations flip bifurcation numerical simulation chaos |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023225?viewType=HTML |
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