论文标题
有限信心模型的广义解决方案
Generalized solutions to bounded-confidence models
论文作者
论文摘要
社会动态中的有界信心模型描述了多代理系统，其中每个人仅在本地与他人进行互动。几个模型被写为具有不连续右侧的普通微分方程的系统：这是将相互作用限制在边界处具有非变化强度的有限区域的直接结果。文献中的各种作品分析了解决方案的特性，例如重中心不变性和聚类。另一方面，从分析的角度，给出解决方案的精确定义的问题经常被忽略。但是，可以提供丰富的文献提出解决方案的不同概念以不连续的微分方程。使用几个解决方案概念，我们展示了如何在一般假设下授予存在，而唯一性甚至在维度上也可能失败，但几乎适用于每个初始条件。因此，解决方案的各种特性取决于使用的定义和初始条件。
Bounded-confidence models in social dynamics describe multi-agent systems, where each individual interacts only locally with others. Several models are written as systems of ordinary differential equations with discontinuous right-hand side: this is a direct consequence of restricting interactions to a bounded region with non-vanishing strength at the boundary. Various works in the literature analyzed properties of solutions, such as barycenter invariance and clustering. On the other side, the problem of giving a precise definition of solution, from an analytical point of view, was often overlooked. However, a rich literature proposing different concepts of solution to discontinuous differential equations is available. Using several concepts of solution, we show how existence is granted under general assumptions, while uniqueness may fail even in dimension one, but holds for almost every initial conditions. Consequently, various properties of solutions depend on the used definition and initial conditions.
