On the stability, chaos and bifurcation analysis of a discrete-time chemostat model using the piecewise constant argument method
In this paper, the dynamics of a discrete-time chemostat model were investigated. The discretization was obtained using the piecewise constant argument method. An analysis was performed to determine the existence and stability of fixed points. In addition, we have shown that the model experiences tr...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241615 |
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| _version_ | 1832590765796098048 |
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| author | Ibraheem M. Alsulami |
| author_facet | Ibraheem M. Alsulami |
| author_sort | Ibraheem M. Alsulami |
| collection | DOAJ |
| description | In this paper, the dynamics of a discrete-time chemostat model were investigated. The discretization was obtained using the piecewise constant argument method. An analysis was performed to determine the existence and stability of fixed points. In addition, we have shown that the model experiences transcritical and period-doubling bifurcations. Two chaos control techniques, feedback control and hybrid control, were employed to control bifurcation and chaos in the model. Moreover, we provided numerical simulations to substantiate our theoretical results. This study illustrates that the piecewise constant argument method is more dynamically consistent than the forward Euler method. |
| format | Article |
| id | doaj-art-a9ea6142a0824161984e4a8ff738bb2e |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-a9ea6142a0824161984e4a8ff738bb2e2025-01-23T07:53:24ZengAIMS PressAIMS Mathematics2473-69882024-11-01912338613387810.3934/math.20241615On the stability, chaos and bifurcation analysis of a discrete-time chemostat model using the piecewise constant argument methodIbraheem M. Alsulami0Mathematics Department, Faculty of Science, Umm Al-Qura University, Makkah 21955, Saudi ArabiaIn this paper, the dynamics of a discrete-time chemostat model were investigated. The discretization was obtained using the piecewise constant argument method. An analysis was performed to determine the existence and stability of fixed points. In addition, we have shown that the model experiences transcritical and period-doubling bifurcations. Two chaos control techniques, feedback control and hybrid control, were employed to control bifurcation and chaos in the model. Moreover, we provided numerical simulations to substantiate our theoretical results. This study illustrates that the piecewise constant argument method is more dynamically consistent than the forward Euler method.https://www.aimspress.com/article/doi/10.3934/math.20241615chemostat modelpiecewise constant argument methodlocal stabilitytranscritical bifurcationperiod-doubling bifurcationchaos control |
| spellingShingle | Ibraheem M. Alsulami On the stability, chaos and bifurcation analysis of a discrete-time chemostat model using the piecewise constant argument method AIMS Mathematics chemostat model piecewise constant argument method local stability transcritical bifurcation period-doubling bifurcation chaos control |
| title | On the stability, chaos and bifurcation analysis of a discrete-time chemostat model using the piecewise constant argument method |
| title_full | On the stability, chaos and bifurcation analysis of a discrete-time chemostat model using the piecewise constant argument method |
| title_fullStr | On the stability, chaos and bifurcation analysis of a discrete-time chemostat model using the piecewise constant argument method |
| title_full_unstemmed | On the stability, chaos and bifurcation analysis of a discrete-time chemostat model using the piecewise constant argument method |
| title_short | On the stability, chaos and bifurcation analysis of a discrete-time chemostat model using the piecewise constant argument method |
| title_sort | on the stability chaos and bifurcation analysis of a discrete time chemostat model using the piecewise constant argument method |
| topic | chemostat model piecewise constant argument method local stability transcritical bifurcation period-doubling bifurcation chaos control |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241615 |
| work_keys_str_mv | AT ibraheemmalsulami onthestabilitychaosandbifurcationanalysisofadiscretetimechemostatmodelusingthepiecewiseconstantargumentmethod |