Hopf bifurcation and center stability for a predator-prey biological economic model with prey harvesting. (English) Zbl 1252.34053
Summary: We investigate Hopf bifurcation and center stability of a predator-prey biological economic model. By employing the local parametrization method, Hopf bifurcation theory and the formal series method, we obtain some testable results on these issues. The economic profit is chosen as a positive bifurcation parameter here. It shows that the phenomenon of Hopf bifurcation occurs as the economic profit increases beyond a certain threshold. Besides, we also find that the center of the biological economic model is always unstable. Finally, some numerical simulations are given to illustrate the effectiveness of our results.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 92D40 | Ecology |
| 92D25 | Population dynamics (general) |
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