论环境波动导致的物种迷失
A remark on the disorienting of species due to the fluctuating environment
摘要：
在这篇文章中，我们研究了稳定的两个物种的社区与趋化性由于短波长的外部信号的原始模式的行为。我们使用Patlak-Keller-Segel类型的系统作为社区的模型。众所周知，这样的系统可以产生复杂的不稳定的行为模式，这通常是数学上解释的一些基本解决方案，描述简单的模式的分叉。据我们所知，在Patlak-Keller-Segel型模型中，所有这样的分叉都是在齐次（即几何不变）系统中发现的，其中基本解是所有物种均质分布的平衡态。本文所考虑的模型不具有平移不变性：假设一个物种（捕食者）能够响应于外部产生的信号以及另一个物种（猎物）发出的信号而移动。例如，外部信号可能会出现从分布的环境特性，如温度，盐度，地形起伏等的不均匀性，我们的目标是检查短波长的不均匀性的影响。为了做到这一点，我们采用了一定的均匀化程序。我们分离的短波长和平滑的系统响应的组件，并导出一个慢系统管理后者之一。分析缓慢的系统，并将其与均匀环境的情况下进行比较表明，一般而言，短波长的不均匀性导致捕食者的运动指数下降。运动性的丧失在很大程度上防止了复杂的不稳定模式的发生，并显著地稳定了原始的基本解。从某种意义上说，处理环境的小规模剧烈变化的必要性使系统无法应对其他挑战。
英文摘要：
In this article we study the stabilizing of a primitive pattern of behaviour for the two-species community with chemotaxis due to the short-wavelength external signal. We use a system of Patlak-Keller-Segel type as a model of the community. It is well-known that such systems can produce complex unsteady patterns of behaviour which are usually explained mathematically by bifurcations of some basic solutions that describe simpler patterns. As far as we aware, all such bifurcations in the models of the Patlak-Keller-Segel type had been found for homogeneous (i.e. translationally invariant) systems where the basic solutions are equilibria with homogeneous distributions of all species. The model considered in the present paper does not possess the translational invariance: one of species (the predators) is assumed to be capable of moving in response to a signal produced externally in addition to the signal emitted by another species (the prey). For instance, the external signal may arise from the inhomogeneity of the distribution of an environmental characteristic such as temperature, salinity, terrain relief, etc. Our goal is to examine the effect of short-wavelength inhomogeneity. To do this, we employ a certain homogenization procedure. We separate the short-wavelength and smooth components of the system response and derive a slow system governing the latter one. Analysing the slow system and comparing it with the case of homogeneous environment shows that, generically, a short-wavelength inhomogeneity results in an exponential decrease in the motility of the predators. The loss of motility prevents, to a great extent, the occurrence of complex unsteady patterns and dramatically stabilizes the primitive basic solution. In some sense, the necessity of dealing with intensive small-scale changes of the environment makes the system unable to respond to other challenges.
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