| Volume 14, Number 5, 2024, Pages - DOI：10.11948/JAAC-2024-0013 |
| Hopf bifurcation and control for the delayed predator-prey model with nonlinear prey harvesting |
| Guodong Zhang,Huangyu Guo,Jing Han |
| Keywords:Stability, Predator–prey system, Time delay, Hopf bifurcation, Periodic solution. |
| Abstract: |
| In our study, we focused on investigating a delayed differential-algebraic system. The system incorporates a square root functional response and non-linear prey harvesting. Employing the normal form of differential algebraic systems and the central manifold theory, we conducted a detailed analysis of the system"s stability and bifurcation phenomena, with time delay identified as a critical bifurcation parameter. When the time delay reached a critical value, the system"s equilibrium points underwent the Hopf bifurcation, resulting in system instability. To achieve stability, we introduced a feedback controller, successfully transitioning the system from an unstable to a stable state. Through subsequent numerical simulations, we validated the accuracy and correctness of our research conclusions. |
PDF Download reader
|
|
|
|