In this paper, we empirically analyze the spatial distribution of Chinese cities using a method based on triangle transition. This method uses a regular triangle mapping from the observed cities and its three neighboring cities to analyze their distribution of mapping positions. We find that obvious center-gathering tendency for the relationship between cities and its nearest three cities, indicating the spatial competition between cities. Moreover, we observed the competitive trends between neighboring cities with similar economic volume, and the remarkable cooperative tendency between neighboring cities with large difference on economy. The threshold of the ratio of the two cities' economic volume on the transition from competition to cooperation is about 1.2. These findings are helpful in the understanding of the cities economic relationship, especially in the study of competition and cooperation between cities.
我们引入了一个模型，在这个模型中，城市人口的增长率与他们的“势力范围”的面积成正比，其中一个城市的影响力取决于它的人口（α次方）和距离城市（β次方），新的城市根据一定的随机规则出现。一个简单的非严格的渐近分析表明，当β> 2α $ the system exhibits "balanced growth" in which there are an increasing number of large cities, whose populations have the same order of magnitude, whereas for β< 2α$时，系统表现出“不平衡增长”，其中少数城市捕获了总人口的大部分。从概念上讲，该模型最好被视为组合的“中国餐馆过程”的空间模拟。
Competition ability dependence on uniqueness in some collaboration-competition bipartite networks
最近，我们的小组定量定义了两个量，“竞争力”和“独特性”（中国。Phys. Lett. 26（2009）058901）为一种合作-竞争的二分网络，其中“生产者”生产一些“产品”并将其“输出”到“市场”以进行竞争。工厂、大学或餐馆都可以作为例子。在信中，我们提出了一个分析结论，竞争能力线性依赖于在平凡的情况下，“输入质量”和“竞争增益”服从正态分布的唯一性。以中国区域大学之间的竞争为例进行了分析。本文讨论了竞争收益服从幂律分布的异常情形。此外，我们将研究扩展到所有的合作-竞争二部网络，从而重新定义了竞争能力。对15个现实世界中的合作竞争系统的竞争能力依赖唯一性进行了实证研究，其中14个属于一般的非平凡情形。我们发现，一般的依赖遵循所谓的“移幂律（SPL）”，但非常接近的幂律。并给出了竞争力分布和独特性分布的异质性指数。这些实证研究将作为未来论文的补充，对非正常合作竞争系统中竞争能力对唯一性的依赖性以及这种依赖性与竞争能力和唯一性异质性之间的关系进行比较和进一步讨论。
