Investigating Global Stability and Bifurcation in an Ecological Dynamical System
We consider a continuous-time model describing the interaction between phytoplankton and zooplankton using a Holling type-II response. We then transform this continuous-time model into a discrete-time counterpart using a fractional-order discretization method. The paper explores the local stability...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2024/4970657 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849686201876873216 |
|---|---|
| author | Muhammad Salman Khan Rizwan Niaz Mohammed Ahmed Alomair Mohamed Hussien |
| author_facet | Muhammad Salman Khan Rizwan Niaz Mohammed Ahmed Alomair Mohamed Hussien |
| author_sort | Muhammad Salman Khan |
| collection | DOAJ |
| description | We consider a continuous-time model describing the interaction between phytoplankton and zooplankton using a Holling type-II response. We then transform this continuous-time model into a discrete-time counterpart using a fractional-order discretization method. The paper explores the local stability of this obtained system concerning all equilibrium points and establishes the global asymptotic stability of its positive fixed point. The study also demonstrates that, under specific mathematical conditions, the system undergoes a Neimark–Sacker bifurcation around its positive equilibrium point. To effectively manage this bifurcation, two modified hybrid control techniques are introduced. The paper concludes by presenting illustrative numerical examples that validate the theoretical findings and assess the effectiveness and feasibility of the newly proposed control strategies. In addition, a comparative analysis is conducted between the modified hybrid techniques and an existing hybrid approach. |
| format | Article |
| id | doaj-art-b82f6eb35df44b7599f6dbcad0bb11e5 |
| institution | DOAJ |
| issn | 1099-0526 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b82f6eb35df44b7599f6dbcad0bb11e52025-08-20T03:22:48ZengWileyComplexity1099-05262024-01-01202410.1155/2024/4970657Investigating Global Stability and Bifurcation in an Ecological Dynamical SystemMuhammad Salman Khan0Rizwan Niaz1Mohammed Ahmed Alomair2Mohamed Hussien3Department of MathematicsDepartment of StatisticsDepartment of Quantitative MethodsDepartment of ChemistryWe consider a continuous-time model describing the interaction between phytoplankton and zooplankton using a Holling type-II response. We then transform this continuous-time model into a discrete-time counterpart using a fractional-order discretization method. The paper explores the local stability of this obtained system concerning all equilibrium points and establishes the global asymptotic stability of its positive fixed point. The study also demonstrates that, under specific mathematical conditions, the system undergoes a Neimark–Sacker bifurcation around its positive equilibrium point. To effectively manage this bifurcation, two modified hybrid control techniques are introduced. The paper concludes by presenting illustrative numerical examples that validate the theoretical findings and assess the effectiveness and feasibility of the newly proposed control strategies. In addition, a comparative analysis is conducted between the modified hybrid techniques and an existing hybrid approach.http://dx.doi.org/10.1155/2024/4970657 |
| spellingShingle | Muhammad Salman Khan Rizwan Niaz Mohammed Ahmed Alomair Mohamed Hussien Investigating Global Stability and Bifurcation in an Ecological Dynamical System Complexity |
| title | Investigating Global Stability and Bifurcation in an Ecological Dynamical System |
| title_full | Investigating Global Stability and Bifurcation in an Ecological Dynamical System |
| title_fullStr | Investigating Global Stability and Bifurcation in an Ecological Dynamical System |
| title_full_unstemmed | Investigating Global Stability and Bifurcation in an Ecological Dynamical System |
| title_short | Investigating Global Stability and Bifurcation in an Ecological Dynamical System |
| title_sort | investigating global stability and bifurcation in an ecological dynamical system |
| url | http://dx.doi.org/10.1155/2024/4970657 |
| work_keys_str_mv | AT muhammadsalmankhan investigatingglobalstabilityandbifurcationinanecologicaldynamicalsystem AT rizwanniaz investigatingglobalstabilityandbifurcationinanecologicaldynamicalsystem AT mohammedahmedalomair investigatingglobalstabilityandbifurcationinanecologicaldynamicalsystem AT mohamedhussien investigatingglobalstabilityandbifurcationinanecologicaldynamicalsystem |