骚乱动力学模型：冲击、扩散和阈值
A model of riots dynamics: shocks, diffusion and thresholds
摘要：
我们介绍和分析了几个变种的微分方程系统的模型的动态社会爆发，如骚乱。该系统涉及耦合的一个明确的变量代表的骚乱活动的强度和潜在的（隐式）领域的社会紧张局势。我们的模型包括外源和内源因素以及各种传播机制的影响。从这些模型的数值和数学分析，我们表明，假设不同的位置如何相互影响，以及如何在系统中的张力分散发挥了重要作用的定性行为的突发社会动荡。此外，我们分析了这些系统的各种性质，如行波解的存在性，并制定了一些新的开放的数学问题，从我们的工作。
英文摘要：
We introduce and analyze several variants of a system of differential equations which model the dynamics of social outbursts, such as riots. The systems involve the coupling of an explicit variable representing the intensity of rioting activity and an underlying (implicit) field of social tension. Our models include the effects of exogenous and endogenous factors as well as various propagation mechanisms. From numerical and mathematical analysis of these models we show that the assumptions made on how different locations influence one another and how the tension in the system disperses play a major role on the qualitative behavior of bursts of social unrest. Furthermore, we analyze here various properties of these systems, such as the existence of traveling wave solutions, and formulate some new open mathematical problems which arise from our work.
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