In this paper, we show the existence of a Hopf bifurcation in a delayed single population model with patch structure. The effect of the dispersal rate on the Hopf bifurcation is considered. Especially, if each patch is favorable for the species, we show that when the dispersal rate tends to zero, the limit of the Hopf bifurcation value is the minimum of the “local” Hopf bifurcation values over all patches. On the other hand, when the dispersal rate tends to infinity, the Hopf bifurcation value tends to that of the “average” model.

中文翻译：

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具有斑块结构的时滞单种群模型的Hopf分支。

在本文中，我们显示了具有补丁结构的延迟单种群模型中存在Hopf分叉。考虑了分散速率对霍普夫分叉的影响。特别是，如果每个斑块都对物种有利，那么我们表明，当扩散速率趋于零时，霍普夫分叉值的极限是所有斑块上“局部”霍普夫分叉值的最小值。另一方面，当分散率趋于无穷大时，霍普夫分叉值趋向于“平均”模型的值。