论文标题
在捕食者捕食模型中具有合作狩猎和合同效应和分叉的全球动力学，由扩散和延迟引起
Global dynamics in a predator-prey model with cooperative hunting and Allee effect and bifurcation induced by diffusion and delays
论文作者
论文摘要
我们考虑具有合作狩猎和合同效应的捕食者捕食模型的局部分叉和全球动态。对于弱合作的模型，我们证明了限制周期的存在，将转换率阈值$ p = p = p = p^{\＃} $。当$ p> p> p^{\＃} $，两个物种都灭绝了，当$ p <p <p^{\＃} $时，有一个sameatrix。初始种群高于分离质的物种最终灭绝了。否则，它们可以可持续地共存或振荡。在强烈合作的情况下，我们在三种不同的情况下表现出系统的复杂动力学，包括极限周期，三个均衡中的杂斜轨道环和同骨周期。此外，我们发现扩散可能会引起图灵的不稳定性和图灵 - 霍普F分叉，从而使系统在空间上具有不均匀分布的物种，并存，两种不同的时空振荡。最后，我们研究了两个延迟引起的扩散系统的HOPF和双HOPF分叉。
We consider the local bifurcation and global dynamics of a predator-prey model with cooperative hunting and Allee effect. For the model with weak cooperation, we prove the existence of limit cycle, heteroclinic cycle at a threshold of conversion rate $p=p^{\#}$. When $p>p^{\#}$, both species go extinct, and when $p<p^{\#}$, there is a separatrix. The species with initial population above the separatrix finally become extinct; otherwise, they coexist or oscillate sustainably. In the case with strong cooperation, we exhibit the complex dynamics of system in three different cases, including limit cycle, loop of heteroclinic orbits among three equilibria, and homoclinic cycle. Moreover, we find diffusion may induce Turing instability and Turing-Hopf bifurcation, leaving the system with spatially inhomogeneous distribution of the species, coexistence of two different spatial-temporal oscillations. Finally, we investigate Hopf and double Hopf bifurcations of the diffusive system induced by two delays.
