论文标题
在社会爆发模型中的行驶波解决方案，以抑制紧张状态
Traveling wave solutions in a model for social outbursts in a tension-inhibitive regime
论文作者
论文摘要
在这项工作中，我们调查了反应扩散系统对社会爆发进行建模的非符号转移波解决方案的存在，例如骚乱活动，最初是在ARXIV中提出的：1502.04725V3。该模型由两个标量值组成，即动乱$ u $的水平和一个张力字段$ v $。该模型的关键组成部分是动荡中的潮流效应，只要张力足够高。我们专注于所谓的张力抑制性制度，其特点是动乱的水平对紧张感具有负面反馈。该制度已被证明与2005年法国骚乱的时空传播具有物理相关。我们使用几何奇异扰动理论来研究这种解决方案在两种情况下的存在。首先是$ u $和$ v $ diffuse以非常小的速率。在这里，观察到的潮流效应的时间尺度起着关键作用。我们考虑的第二种情况是，张力以比动乱水平慢得多的速度扩散。在这种情况下，我们能够推断出驾驶动力学是由众所周知的Fisher-KPP方程建模的。
In this work we investigate the existence of non-monotone traveling wave solutions to a reaction-diffusion system modeling social outbursts, such as rioting activity, originally proposed in arXiv:1502.04725v3. The model consists of two scalar values, the level of unrest $u$ and a tension field $v$. A key component of the model is a bandwagon effect in the unrest, provided the tension is sufficiently high. We focus on the so-called tension inhibitive regime, characterized by the fact that the level of unrest has a negative feedback on the tension. This regime has been shown to be physically relevant for the spatiotemporal spread of the 2005 French riots. We use Geometric Singular Perturbation Theory to study the existence of such solutions in two situations. The first is when both $u$ and $v$ diffuse at a very small rate. Here, the time scale over which the bandwagon effect is observed plays a key role. The second case we consider is when the tension diffuses at a much slower rate than the level of unrest. In this case, we are able to deduce that the driving dynamics are modeled by the well-known Fisher-KPP equation.
