Rise of nations: Why do empires expand and fall?
Rise of nations: Why do empires expand and fall?
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DOI：
10.1063/5.0004795
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发表时间：
2020-09
期刊：
影响因子：
2.9
通讯作者：
Sergey Vakulenko;D. Lyakhov;Andreas Weber;D. Lukichev;Dominik L. Michels
中科院分区：
文献类型：
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作者：
Sergey Vakulenko;D. Lyakhov;Andreas Weber;D. Lukichev;Dominik L. Michels
我们考虑由多颗卫星组成的集中网络，这些卫星围绕着几个占主导地位的超利己中心。这些所谓的帝国是利用分而治之的框架组织起来的，该框架实施了强大的中心-卫星互动，同时保持卫星之间的成对互动足够弱。我们给出了一个随机稳定性分析，其中我们认为这些动力系统是稳定的，如果中心有足够的资源，而卫星没有价值。我们的模型基于一个Hopfield类型的网络，该网络证明了它在人工智能领域的重要性。使用该模型表明，分而治之的框架提供了重要的优势：它允许通过调整中心-卫星相互作用以直接的方式完全控制动态。此外，研究表明，这样的帝国应该只有一个统治中心，以提供足够的稳定性。为了生存，帝国应该有转换机制，通过选择适当的本地吸引者来实施适当的行为模式，以便正确地应对内部和外部的挑战。通过与玻色-爱因斯坦凝聚的类比，我们证明了如果每对节点的噪声关联为负，那么关于噪声最稳定的结构是一个全局连通网络。对于社会系统，我们证明只有在中心缓慢演化的情况下，才有可能通过中心进行控制。除了状态接近某一稳定状态的短时间外，这种结构的发展是非常缓慢的，并且与系统结构的大小负相关。因此，不断扩大的规模最终会落入“控制陷阱”。
We consider centralized networks composed of multiple satellites arranged around a few dominating super-egoistic centers. These so-called empires are organized using a divide and rule framework enforcing strong center–satellite interactions while keeping the pairwise interactions between the satellites sufficiently weak. We present a stochastic stability analysis, in which we consider these dynamical systems as stable if the centers have sufficient resources while the satellites have no value. Our model is based on a Hopfield type network that proved its significance in the field of artificial intelligence. Using this model, it is shown that the divide and rule framework provides important advantages: it allows for completely controlling the dynamics in a straight-forward way by adjusting center–satellite interactions. Moreover, it is shown that such empires should only have a single ruling center to provide sufficient stability. To survive, empires should have switching mechanisms implementing adequate behavior models by choosing appropriate local attractors in order to correctly respond to internal and external challenges. By an analogy with Bose–Einstein condensation, we show that if the noise correlations are negative for each pair of nodes, then the most stable structure with respect to noise is a globally connected network. For social systems, we show that controllability by their centers is only possible if the centers evolve slowly. Except for short periods when the state approaches a certain stable state, the development of such structures is very slow and negatively correlated with the size of the system’s structure. Hence, increasing size eventually ends up in the “control trap.”