A Leslie–Gower predator–prey model with square root response function and generalist predator is considered, and the existence and stability of equilibria of the system are discussed. It is shown that the system undergoes a degenerate Hopf bifurcation of codimension exactly two, where there exist two limit cycles. In addition, we find that the system has a cusp of codimension two and exhibits a Bogdanov–Takens bifurcation of codimension two. Our results reveal richer dynamics than the system with no generalist predator.

中文翻译：

---

具有平方根响应函数和通才捕食者的 Lesile-Gower 捕食者-被捕食者模型的动力学


考虑具有平方根响应函数和通才捕食者的Leslie-Gower捕食者-被捕食者模型，并讨论了系统平衡的存在性和稳定性。结果表明，系统经历了正好二维的简并 Hopf 分岔，其中存在两个极限环。此外，我们发现该系统具有余维二的尖点，并表现出余维二的波格丹诺夫-塔肯斯分叉。我们的结果揭示了比没有通才捕食者的系统更丰富的动态。