The economic agglomeration of one large city surrounded by satellite cities is observed worldwide and is a topic of keen economic interest. We theoretically investigate where such satellite cities emerge in a two-dimensional economic space in which discrete locations are evenly distributed in a regular-hexagonal domain. To elucidate this emergence, we introduce two viewpoints: (1) the bifurcation mechanism of the full agglomeration at the geographical center in this domain (mono-center), which produces satellite cities around this center, and (2) the existence of invariant patterns, which are equilibria for any value of the transport cost parameter. Theoretically-predicted agglomeration patterns are ensured to exist as stable equilibria for a spatial economic model proposed by Forslid and Ottaviano (2003). We theoretically find one large central city surrounded by hexagonal satellite cities that is a two-dimensional counterpart of the core-periphery pattern (Krugman 1991). Moreover, we demonstrate that spatial patterns of twin cities, three cities, and racetrack cities are absorbed into the mono-center as the transport cost decreases. These transitions are ubiquitously observed in the two-dimensional spatial platform with the geographical center.

一个大城市被卫星城市包围的经济集聚在世界范围内都是观察到的，是一个经济利益浓厚的话题。我们从理论上研究了此类卫星城市出现在二维经济空间中的位置，其中离散位置均匀分布在正六边形域中。为了阐明这种出现，我们引入了两个观点：（1）该域地理中心（单中心）的完全集聚的分叉机制，在该中心周围产生卫星城市，以及（2）不变模式的存在，这是运输成本参数的任何值的均衡。Forslid 和 Ottaviano（2003 年）提出的空间经济模型可确保理论上预测的集聚模式作为稳定均衡存在。从理论上讲，我们发现一个大型中心城市被六边形卫星城市包围，这是核心-边缘模式的二维对应物 (Krugman 1991)。此外，我们证明了随着交通成本的降低，双城、三城和赛马城的空间格局被吸收到单中心。这些转变在具有地理中心的二维空间平台中无处不在。