Abstract: Opening to the outside world is one of the fundamental national policies in China.Since the enact of the reform and opening policy,China has gradually formed the comprehensive,multi-level,and wide-ranging opening structure to the outside world,which has brought tremendous and impressive achievements.Since 1978,China has attracted more than 1.7 trillion US dollars of foreign investment,and has reached the cumulative direct foreign investment of more than 1.2 trillion US dollars,which contribute greatly to the development of global economies.In this paper,by analyzing the economic data from the 343 Chinese administrative region cities of the prefecture-level and the above,the entropy-mutation model was established based on the dependence-level of the economic-opening-degree on the foreign trade,investment,tourism and other indicators,leading to the comprehensive assessment on the opening degree of these cities.Through the methods of ESDA,three-dimensional interpolation fitting analyses,barycenter shifting,and space transform function,this paper discussed the overall trends of economic-opening-degree of these aforementioned cities,and the evolutionary characteristics and mechanism of its spatial pattern during 2005-2015 from the perspective of space-time coupling.The results showed as follows:(1) the Chinese economic-opening-degree obviously showed multiple characteristics directed by administration,spatial zone,and regional-opening.Municipalities,sub-provincial cities and capital cities had high economic-opening-degree to the outside world.Marginal differences were observed among these prefecture-level cities.The economic-opening-degree decreased from the East to the Central,Northeast and the West China respectively.The South China had a higher opening degree than the North.Special economic zones and coastal opening cities showed a high level of opening.Meanwhile,river-along and inland opening cities steadily increased their opening degree but have significant difference.(2) The opening degree was significantly related with spatial zones and showed the club characteristics of the small cities of scattering and the large cities of gathering.From 2005 to 2015,the economic opening maintained a relatively overall stable status with the opening degree improving,closing degree declining,and the overall degree of plateau type distributing sparsely.(3) The random change of China's economic opening degree structure is gradually vanishing.The spatial self-organization and continuity of opening degree's structure were more significant.Better homogeneous structure of the opening degree was observed in the Northeast over the Southwest.Clear spatial differences between the Southeast and the Northwest were showed.As the representatives of regional economic development,the prefecture-level cities are organizers,directors,and controllers.Through the research of economic-opening-degree of these cities,this paper could provide scientific advises for the government to make reasonable opening strategies to the outside world and promote regional harmony-development in the new economic situation.

Key words: opening rate, catastrophe progression method, ESDA-GIS, spatial-temporal differentiation, China