[1] Alves D, Barreira A P, Guimaraes M H et al., 2016. Historical trajectories of currently shrinking Portuguese cities: a typology of urban shrinkage. Cities, 52: 20–29. doi:  10.1016/j.cities.2015.11.008
[2] Baccalá L A, Sameshima K, 2001. Overcoming the limitations of correlation analysis for many simultaneously processed neural structures. Progress in Brain Research, 130: 33–47. doi:  10.1016/S0079-6123(01)30004-3
[3] Billings S A, 2013. Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. Chichester: Wiley, 549–555.
[4] Blanco H, Alberti M, Forsyth A et al., 2009. Hot, congested, crowded and diverse: emerging research agendas in planning. Progress in Planning, 71(4): 153–205. doi:  10.1016/j.progress.2009.03.001
[5] Bontje M, 2001. Dealing with deconcentration: population deconcentration and planning response in polynucleated urban regions in north-west Europe. Urban Studies, 38(4): 769–785. doi:  10.1080/00420980120035330
[6] Bontje M, 2004. Facing the challenge of shrinking cities in east Germany: the case of Leipzig. Geojournal, 61(1): 13–21. doi:  10.1007/s10708-005-0843-2
[7] Camarda D, Rotondo F, Selicato F, 2015. Strategies for dealing with urban shrinkage: issues and scenarios in Taranto. European Planning Studies, 23(1): 126–146.
[8] Deng Yanru, Zhang Mingdou, 2020. Heterogeneous city shrinkage and urban public service level-Also on the regulatory role of Economic development level. Soft Science, 34(12): 96–103. (in Chinese)
[9] Department of Urban Surveys of National Bureau of Statistics of China, 2006–2020. China City Statistical Yearbook. Beijing: China Statistics Press. (in Chinese)
[10] Du Zhiwei, Li Xun, 2018. Characteristic and Mechanism of urban growth and shrinkage from demographic change perspective: a case study of Dongguan. Scientia Geographica Sinica, 38(11): 1837–1846. (in Chinese)
[11] Du Z W, Jin L X, Ye Y Y et al., 2020a. Characteristics and influences of urban shrinkage in the Exo-urbanization area of the Pearl River Delta, China. Cities, 103: 102767. doi:  10.1016/j.cities.2020.102767
[12] Du Zhiwei, Jin Lixia, Zhang Hongou, 2020b. Planning response and implications for urban vacancy with the experience of smart shrinkage in Germany, America, and Japan. Urban Planning International, 35(2): 29–37. (in Chinese)
[13] Feldhoff T, 2013. Shrinking communities in Japan: community ownership of assets as a development potential for rural Japan. URBAN DESIGN International, 18(1): 99–109. doi:  10.1057/udi.2012.26
[14] Forrester J W, 2003. Dynamic models of economic systems and industrial organizations. System Dynamics Review, 19(4): 329–345. doi:  10.1002/sdr.284
[15] Gatzweiler H P, Meyer K, Milbert A, 2003. Schrumpfende stäte in Deutschland? Fakten und trends. Informationen zur Rau mentwieklung, 11(24): 557–574. doi:  10.1007/BF03183060
[16] Gao Shuqi, Long Ying, 2017. Distinguishing and planning shrinking cities in northeast China. Planners, 33(1): 26–32. (in Chinese)
[17] Guimaraes M H, Nunes L C, Barreira A P et al., 2016. What makes people stay in or leave shrinking cities? An empirical study from Portugal. European Planning Studies, 24(9): 1684–1708. doi:  10.1080/09654313.2016.1177492
[18] Guo Yuanyuan, Li Li, 2019. Change in the negative externality of the shrinking cities in China. Scientia Geographica Sinica, 39(1): 52–60. (in Chinese)
[19] Haase A, Rink D, Grossmann K et al., 2014. Conceptualizing urban shrinkage. Environment and Planning A:Economy and Space, 46(7): 1519–1534. doi:  10.1068/a46269
[20] Haase A, Bernt M, Großmann K et al., 2016. Varieties of shrinkage in European cities. European Urban and Regional Studies, 23(1): 86–102. doi:  10.1177/0969776413481985
[21] Hartt M D, 2018a. How cities shrink: complex pathways to population decline. Cities, 75: 38–49. doi:  10.1016/j.cities.2016.12.005
[22] Hartt M D, 2018b. The diversity of north American shrinking cities. Urban Studies, 55(13): 2946–2959. doi:  10.1177/0042098017730013
[23] He S Y, Lee J, Zhou T et al., 2017. Shrinking cities and resource-based economy: the economic restructuring in China’s mining cities. Cities, 60: 75–83. doi:  10.1016/j.cities.2016.07.009
[24] Hegang Bureau of Statistics, 2006−2020. Hegang Statistical Yearbook. Beijing: China Statistics Press. (in Chinese)
[25] Hegang Bureau of Statistics, 2005−2019. Statistical bulletin of national economic and social development of Hegang City, http://www.tjcn.org/tjgb/08hlj/946.html. Cited 8 September 2021. (in Chinese)
[26] Hegang Municipal People’s Government. Main data bulletin of the seventh national census of Hegang City in 2020. Available at: www.hegang.gov.cn/xxgk_new/z_xgknr/z_xgjxx/z_xtjgb/2021/03/36138.htm. 2021-06-01
[27] Heilongjiang Bureau of Statistics, 2006–2020. Heilongjiang Statistical Yearbook. Beijing: China Statistics Press. (in Chinese)
[28] Hoekveld J J, 2012. Time-space relations and the differences between shrinking regions. Built Environment, 38(2): 179–195. doi:  10.2148/benv.38.2.179
[29] Huang Weiting, 2014. Research on the shrinking cities in UK and the revelation to China. Planners, 30(S5): 205–209. (in Chinese)
[30] Jiang Haining, Zhang Wenzhong, Yu Jianhui et al., 2020. Spatial coupling of innovative milieu and industrial structure transformation of resource-based cities in Shanxi province. Journal of Natural Resources, 35(2): 269–283. (in Chinese)
[31] Jin Xianfeng, Dong Suocheng, Liu Wei et al., 2010. Study on relationship between industrial chain extension and evolution of resource-based City-A case study on Tongling City. Economic Geography, 30(3): 403–408. (in Chinese)
[32] Khavarian-Garmsir A R, Pourahmad A, Hataminejad H et al., 2018. A comparative assessment of economic and physical inequality between shrinking and growing cities: a case study of Khuzestan province, Iran. International Journal of Urban Sciences, 22(1): 104–122. doi:  10.1080/12265934.2017.1358653
[33] Kim J M, Jung Y S, Choi T et al., 2011. Partial correlation with copula modeling. Computational Statistics & Data Analysis, 55(3): 1357–1366. doi:  10.1016/j.csda.2010.09.025
[34] Koster H R A, Rouwendal J, 2012. The impact of mixed land use on residential property values. Journal of Regional Science, 52(5): 733–761. doi:  10.1111/j.1467-9787.2012.00776.x
[35] Lee J S, Won S, Kim S, 2016. Describing changes in the built environment of shrinking cities: case study of Incheon, south Korea. Journal of Urban Planning and Development, 142(2): 05015010. doi:  10.1061/(ASCE)UP.1943-5444.0000305
[36] Li B, Dewan H, 2017. Efficiency differences among China’s resource-based cities and their determinants. Resources Policy, 51: 31–38. doi:  10.1016/j.resourpol.2016.11.003
[37] Li He, Mykhnenko V, 2018. Urban shrinkage with Chinese characteristics. The Geographical Journal, 184(4): 398–412. doi:  10.1111/geoj.12266
[38] Li He, Kevin L, Zhang Pingyu, 2020. Population shrinkage in resource-dependent cities in China: processes, patterns and drivers. Chinese Geographical Science, 30(1): 1–15. doi:  10.1007/s11769-019-1077-4
[39] Li Hong, Zou Qing, 2018. Environmental regulations, resource endowments and urban industry transformation: comparative analysis of resource-based and non-resource-based cities. Economic Research Journal, 53(11): 182–198. (in Chinese)
[40] Lin Xiongbin, Yang Jiawen, Zhang Xianchun et al., 2017. Measuring shrinking cities and influential factors in urban China: perspective of population and economy. Human Geography, 32(1): 82–89. (in Chinese)
[41] Liu Chunyang, Yang Peifeng, 2017. A comparative study on the motivation mechanism and performance characteristics of Chinese and Foreign shrinking cities. Modern Urban Research, (3): 64–71. (in Chinese)
[42] Liu Wenxin, Zhang Pingyu, Ma Yanji, 2007. Environmental effects of industrial structure evolution of resources-based city: a case study of Anshan city. Journal of Arid Land Resources and Environment, 21(2): 17–21. (in Chinese)
[43] Liu X J, Long Y, 2016. Automated identification and characterization of parcels with OpenStreetMap and points of interest. Environment and Planning B:Planning and Design, 43(2): 341–360.
[44] Liu Yubo, Li Jian, Xiao Suping et al., 2020. How does urban shrinkage affect the supply of local public services. Urban Development Studies, 27(7): 11–18. (in Chinese)
[45] Long R Y, Chen H, Li H J et al., 2013. Selecting alternative industries for Chinese resource cities based on intra-and inter-regional comparative advantages. Energy Policy, 57: 82–88. doi:  10.1016/j.enpol.2012.10.047
[46] Long Ying, Wu Kang, Wang Jianghao, 2015. Shrinking Cities in China. Modern Urban Research, (9): 14–19. (in Chinese)
[47] Long Y, Wu K, 2016. Shrinking cities in a rapidly urbanizing China. Environment and Planning A:Economy and Space, 48(2): 220–222. doi:  10.1177/0308518X15621631
[48] Mallach A, 2017. What we talk about when we talk about shrinking cities: the ambiguity of discourse and policy response in the United States. Cities, 69: 109–115. doi:  10.1016/j.cities.2017.01.008
[49] Meng Xiangfeng, Wang Dongyan, Li Hong, 2019. Correlation between urban shrink and urban compactness ratio in old industrial city: taking Siping city in Jilin province as an example. Economic Geography, 39(4): 67–74. (in Chinese)
[50] Miao Changhong, Hu Zhiqiang, Geng Fengjuan et al., 2018. Characteristics of economic evolution and the influencing factors of resource-dependent cities in China: the role of path dependence, vulnerability and path creation. Geographical Research, 37(7): 1268–1281. (in Chinese)
[51] Ministry of Housing and Urban-Rural Development of the People’s Republic of China, 2006−2020. China Urban Construction Statistical Yearbook. Beijing: China Statistics Press. (in Chinese)
[52] Nefs M, Alves S, Zasada I et al., 2013. Shrinking cities as retirement cities? Opportunities for shrinking cities as green living environments for older individuals. Environment and planning A:Economy and Space, 45(6): 1455–1473. doi:  10.1068/a45302
[53] Park T, Shao X F, Yao S, 2015. Partial martingale difference correlation. Electronic Journal of Statistics, 9(1): 1492–1517. doi:  10.1214/15-EJS1047
[54] Reckien D, Martinez-Fernandez C, 2011. Why do cities shrink. European Planning Studies, 19(8): 1375–1397. doi:  10.1080/09654313.2011.593333
[55] Rieniets T, 2009. Shrinking cities: causes and effects of urban population losses in the twentieth century. Nature and Culture, 4(3): 231–254. doi:  10.3167/nc.2009.040302
[56] Saeed K, 2014. Jay Forrester’s operational approach to economics. System Dynamics Review, 30(4): 233–261. doi:  10.1002/sdr.1525
[57] Shao Peng, Wang Qi, Shan Yingji, 2020. Research on ecological protection and high quality development of Yellow River Basin based on text analysis. Journal of Arid Land Resources and Environment, 34(11): 78–83. (in Chinese)
[58] Sousa S, Pinho P, 2015. Planning for shrinkage: paradox or paradigm. European Planning Studies, 23(1): 12–32. doi:  10.1080/09654313.2013.820082
[59] Sun Wei, Li Yang, Wang Dai et al., 2012. The efficiencies and their changes of China’s resources-based cities employing DEA and Malmquist index models. Journal of Geographical Science, 22(3): 509–520. doi:  10.1007/s11442-012-0943-0
[60] Sun Yang, Jiang Yuanxiang, Zhao Xiang et al., 2010. Survey on the research of network visualization. Computer Science, 37(2): 12–18,30. (in Chinese)
[61] Tan Juntao, Zhang Pingyu, Lo K et al., 2017. Conceptualizing and measuring economic resilience of resource-based cities: case study of Northeast China. Chinese Geographical Science, 27(3): 471–481. doi:  10.1007/s11769-017-0878-6
[62] Vargha A, Bergman L R, Delaney H D, 2013. Interpretation problems of the partial correlation with nonnormally distributed variables. Quality & Quantity, 47(6): 3391–3402. doi:  10.1007/s11135-012-9727-y
[63] Wang Changjun, Qu Yangyang, Wu Xiangli, 2019. A study on economic-population contraction governance in resource-exhausted cities: a realistic analysis based on resource-exhausted cities in Heilongjiang Province. Macroeconomics, (8): 156–169. (in Chinese)
[64] Wang Jie, Ye Jianping, 2020. Population and housing market in shrinking cities with declining industries: based on analysis in Dongguan City. Urban Problems, (6): 56–63. (in Chinese)
[65] Wang Lucang, Chang Fei, 2019. Public service facilities configuration and planning based on multi-source data, Lanzhou. Planners, 35(18): 12–18. (in Chinese)
[66] Wen Jun, Zhao Xufeng, 2007. The relationship between China’s stock market, real estate market and economic growth. Statistics & Decision, (20): 90–92. (in Chinese)
[67] Wiechmann T, Pallagst K M, 2012. Urban shrinkage in Germany and the USA: a comparison of transformation patterns and local strategies. International Journal of Urban and Regional Research, 36(2): 261–280. doi:  10.1111/j.1468-2427.2011.01095.x
[68] Wolff M, Wiechmann T, 2018. Urban growth and decline: Europe’s shrinking cities in a comparative perspective 1990–2010. European Urban and Regional Studies, 25(2): 122–139. doi:  10.1177/0969776417694680
[69] Wu Kang, Long Ying, Yang Yu, 2015. Urban shrinkage in the Beijing-Tianjin-Hebei region and Yangtze River delta: pattern, trajectory and factors. Modern Urban Research, (9): 26–35. (in Chinese)
[70] Wu Kang, Sun Dongqi, 2017. Progress in urban shrinkage research. Economic Geography, 37(11): 59–67. (in Chinese)
[71] Wu Kang, Qi Wei, 2021. Shrinking cities: misunderstandings, identifications and reflections. Geographical Research, 40(1): 213–229. (in Chinese)
[72] Wu K, Wang X N, 2020. Understanding growth and shrinkage phenomena of industrial and trade cities in southeastern China: case study of Yiwu. Journal of Urban Planning and Development, 146(4): 05020028. doi:  10.1061/(ASCE)UP.1943-5444.0000628
[73] Wu K, Yao C C, 2021. Exploring the association between shrinking cities and the loss of external investment: an intercity network analysis. Cities, 119: 103351. doi:  10.1016/j.cities.2021.103351
[74] Xie Yuantao, Li Hong, Zou Qing, 2017. A study on the innovation index of resource-based cities in China: taking 116 cities at the prefecture level for example. Journal of Peking University (Philosophy & Social Sciences), 54(5): 146–158. (in Chinese)
[75] Xu Bo, Pang Deliang, 2014. Growth and decline: a study on the international urban shrinkage and its enlightenment to China. Economist, (4): 5–13. (in Chinese)
[76] Yang Dongfeng, Long Ying, Yang Wenshi et al., 2015. Losing population with expanding space: paradox of urban shrinkage in China. Modern Urban Research, (9): 20–25. (in Chinese)
[77] Yang W, Jiang X L, 2018. Evaluating sustainable urbanization of resource-based cities based on the Mckinsey matrix: case study in China. Journal of Urban Planning and Development, 144(1): 05017020. doi:  10.1061/(ASCE)UP.1943-5444.0000423
[78] Yang Y, Yan Z, Yeh A G O et al., 2017. Measurements of POI-based mixed use and their relationships with neighbourhood vibrancy. International Journal of Geographical Information Science, 31(4): 658–675. doi:  10.1080/13658816.2016.1220561
[79] Yang Z S, Dunford M, 2018. City shrinkage in China: scalar processes of urban and hukou population losses. Regional Studies, 52(8): 1111–1121. doi:  10.1080/00343404.2017.1335865
[80] Yu Binbin, 2015. Economic growth effects of industrial restructuring and productivity improvement: analysis of dynamic spatial panel model with Chinese city data. China Industrial Economics, (12): 83–98. (in Chinese)
[81] Yu C, De Jong M, Cheng B D, 2016. Getting depleted resource-based cities back on their feet again: the example of Yichun in China. Journal of Cleaner Production, 134: 42–50. doi:  10.1016/j.jclepro.2015.09.101
[82] Yu Jianhui, Zhang Wenzhong, Wang Dai et al., 2013. The effect of resource-exhausted city transformation. Resources Science, 35(9): 1812–1820. (in Chinese)
[83] Zhang Cheng, Cai Wanhuan, Yu Tongshen, 2013. Regional economic development and carbon productivity——a convergent and decoupling index analysis. China Industrial Economics, (5): 18–30. (in Chinese)
[84] Zhang Jie, Guo Cheng, 2016. Dealing with shrinking city in Germany: a case of Leipzig. Modern Urban Research, (2): 11–16. (in Chinese)
[85] Zhang Xueliang, Zhang Mingdou, Xiao Hang, 2018. Study on spatial pattern and formation mechanism of urban contraction in Chengdu-Chongqing city cluster. Journal of Chongqing University (Social Science Edition), 24(6): 1–14. (in Chinese)
[86] Zhang Yong, 2015. Will the real estate market crush China: a Study on the dynamic relationship between real estate market, money market fluctuation and economic fluctuation. Public Finance Research, (9): 8–22. (in Chinese)
[87] Zhong Shaoying, Yang Xin, Chen Rui, 2016. The accessibility measurement of hierarchy public service facilities based on multi-mode network dataset and the two-step 2SFCA: a case study of Beijing’s medical facilities. Geographical Research, 35(4): 731–744. (in Chinese)
[88] Zhou Kai, Qian Fangfang, Yan Yan, 2017. A multi-scaled analysis of the ‘Shrinking Map’ of the population in Hunan province. Geographical Research, 36(2): 267–280. (in Chinese)