动力系统中的核晕不稳定性
Core-halo instability in dynamical systems
摘要：
本文证明了动力系统的一个不稳定性定理。当人们在一个复杂系统中的子系统之间增加相互作用时，结构化的或随机的，达到了连接的阈值，超过该阈值，整体动态不可避免地变得不稳定。门槛值出现在子系统之间的流动和相互作用（“表面”效应）压倒内部稳定动态（“体积”效应）的点上。该定理用于确定具有核心-晕或核心-外围结构的系统中的不稳定性阈值，包括重力-热灾难-即，恒星崩溃和爆炸--以及银行间支付网络。在核心-晕模型中，引力和金融崩溃的基础都是同样的动力学不稳定性。
英文摘要：
This paper proves an instability theorem for dynamical systems. As one adds interactions between subystems in a complex system, structured or random, a threshold of connectivity is reached beyond which the overall dynamics inevitably goes unstable. The threshold occurs at the point at which flows and interactions between subsystems (`surface' effects) overwhelm internal stabilizing dynamics (`volume' effects). The theorem is used to identify instability thresholds in systems that possess a core-halo or core-periphery structure, including the gravo-thermal catastrophe -- i.e., star collapse and explosion -- and the interbank payment network. In the core-halo model, the same dynamical instability underlies both gravitational and financial collapse.
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