{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T16:42:41Z","timestamp":1777653761688,"version":"3.51.4"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2012,12,20]],"date-time":"2012-12-20T00:00:00Z","timestamp":1355961600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A spatial approach that incorporates three economic components and one environmental factor has been developed to evaluate the dynamic behaviours of the rural areas at a provincial level. An artificial fish swarm algorithm with variable population size (AFSAVP) is proposed for the spatial problem. A functional region affecting index \u03b8 is employed as a fitness function for the AFSAVP driven optimisation, in which a gross domestic product (GDP) based method is utilised to estimate the CO2 emission of all provinces. A simulation for the administrative provinces of China has been implemented, and the results have shown that the modelling method based on GDP data can assess the spatial dynamic behaviours and can be taken as an operational tool for the policy planners.<\/jats:p>","DOI":"10.3390\/e15010010","type":"journal-article","created":{"date-parts":[[2012,12,20]],"date-time":"2012-12-20T11:27:57Z","timestamp":1356002877000},"page":"10-31","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Quantitative Analysis of Dynamic Behaviours of Rural Areas at Provincial Level Using Public Data of Gross Domestic Product"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7960-8374","authenticated-orcid":false,"given":"Yi","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mechatronics Engineering, University of Electronic Science and Technology of China,Chengdu, 611731, China"},{"name":"School of Engineering and Built Environment, Glasgow Caledonian University, Glasgow,G4 0BA, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangfeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"GREQAM, School of Economics, Aix-Marseille University, Marseille, 13236, France"},{"name":"Department of Economics, Adam Smith Business School, University of Glasgow, Glasgow,G12 8RT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiyang","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong,ShaTin, New Territories, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Zheng","sequence":"additional","affiliation":[{"name":"Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences,Chongqing 401120, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Miao","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering, University of Electronic Science and Technology of China,Chengdu, 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,12,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1038\/4351179a","article-title":"China\u2019s environment in a globalizing world","volume":"435","author":"Liu","year":"2005","journal-title":"Nature"},{"key":"ref_2","unstructured":"Peters, G., Weber, C., and Liu, J.R. (2006). 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