具有Allee效应的空间结构种群中的多吸引子和长瞬变
Multiple attractors and long transients in spatially structured populations with an Allee effect
摘要：
我们提出了一个离散时间模型的空间结构人口和探索耦合的影响时，当地的动态包含一个强大的Allee效应和过补偿。一个孤立的种群只能表现出双稳态和本质灭绝，而一个空间结构化的种群可以表现出许多共存的吸引子。我们确定的机制和参数范围，可以保护空间结构的人口从本质上灭绝，而它是不可避免的本地系统。在弱耦合的情况下，一个亚布居密度高于Allee阈值而另一个低于Allee阈值的状态可以防止本质灭绝。强耦合，另一方面，使两个人口持续高于Allee阈值时，动态（近似）的相位。在这两种情况下，吸引子具有分形盆地边界。在这些参数范围之外，没有发现扩散可以防止基本灭绝。我们还展示了空间结构如何导致人口灭绝之前的持久性长瞬变。
英文摘要：
We present a discrete-time model of a spatially structured population and explore the effects of coupling when the local dynamics contain a strong Allee effect and overcompensation. While an isolated population can exhibit only bistability and essential extinction, a spatially structured population can exhibit numerous coexisting attractors. We identify mechanisms and parameter ranges that can protect the spatially structured population from essential extinction, whereas it is inevitable in the local system. In the case of weak coupling, a state where one subpopulation density lies above and the other one below the Allee threshold can prevent essential extinction. Strong coupling, on the other hand, enables both populations to persist above the Allee threshold when dynamics are (approximately) out-of-phase. In both cases, attractors have fractal basin boundaries. Outside of these parameter ranges, dispersal was not found to prevent essential extinction. We also demonstrate how spatial structure can lead to long transients of persistence before the population goes extinct.
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