Global dynamics analysis of a water hyacinth fish ecological system under impulsive control
- Publisher:
- Elsevier
- Publication Type:
- Journal Article
- Citation:
- Journal of the Franklin Institute, 2022, 359, (18), pp. 10628-10652
- Issue Date:
- 2022-12-01
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| Filename | Description | Size | |||
|---|---|---|---|---|---|
| Global Dynamics Analysis of water hyacinth.pdf | 1.59 MB |
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Control of a water hyacinth-fish ecological system is required for a healthy and sustainable environment. This paper aims to investigate the global dynamics of a water hyacinth fish ecological system under ratio-dependent state impulsive control. First, we study the positivity and boundedness of the solution of the controlled system. By studying the local stability of the equilibrium, we find that the system has two situations. One is that there are two equilibria, namely a saddle point and a boundary equilibrium. In the second case, there are four equilibria, namely, two saddle points, a boundary equilibrium, and a focus point. For the first case, when we select an appropriate ratio-dependent control threshold, the trajectory will globally converge to the boundary equilibrium. For the second case, when the control line is located below the focus point, by using Poincare mapping method, flip bifurcation theory, and vector field analysis techniques, we find that the solution of the controlled system either globally converges to the boundary equilibrium, order-1 periodic solution, or order-2 periodic solution under certain conditions. When the control line is located above the focus point, the solution of the controlled system either globally converges to the focus point, order-1 or order-2 periodic solution. Finally, we use examples to verify the correctness and validity of the theoretical results.
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