资源-环境-经济(REE)模型的非线性动力学分析
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摘要
为了寻找可持续的发展道路,探索不同发展模式下的生态环境效应,为可持续发展战略提供理论依据,推动构建环境友好型社会,建立了一个考虑环境污染治理的"资源-环境-经济"(REE)三维动力系统模型,利用非线性动力学理论及数值模拟的方法,理论分析了系统的局部稳定性,对系统的动力学行为进行了数值模拟,着重对污染排放和资源提取这两个重要因素进行研究,讨论其对系统的影响.结果表明,污染排放率和资源提取率对系统有很大影响.当污染排放率在一定范围时,系统出现极限环,形成周期现象.当资源提取率控制到一定范围内,可使经济达到稳定水平的同时,减少环境污染,保证资源储量.此研究对实现"资源-环境-经济"的协调可持续发展具有重要的现实意义.
In order to find the sustainable development model and reveal the environmental effects of different development models,this paper provides a theoretical basis for the sustainable development and environmentfriendly society construction. This paper establishes a "resource-environment-economy"( REE) three-dimensional Dynamic system model,and the nonlinear stability of the system is analyzed by nonlinear dynamic theory and numerical simulation. The dynamic behavior of the system is simulated numerically,and the two important factors of pollution emission and resource extraction are studied emphatically to discuss their impact on the system. The results show that the pollution rate and resource extraction rate have a great influence on the system. When the pollution emission rate is in a certain range,the system appears limiting ring and forms the periodic phenomena.When the resource extraction rate is controlled to a certain extent,the economy can achieve a stable level,environmental pollution is also reduced and resource reserves are ensured. This paper has important practical significance to realize the coordinated and sustainable development of "resource-environment-economy".
In order to find the sustainable development model and reveal the environmental effects of different development models,this paper provides a theoretical basis for the sustainable development and environmentfriendly society construction. This paper establishes a "resource-environment-economy"( REE) three-dimensional Dynamic system model,and the nonlinear stability of the system is analyzed by nonlinear dynamic theory and numerical simulation. The dynamic behavior of the system is simulated numerically,and the two important factors of pollution emission and resource extraction are studied emphatically to discuss their impact on the system. The results show that the pollution rate and resource extraction rate have a great influence on the system. When the pollution emission rate is in a certain range,the system appears limiting ring and forms the periodic phenomena.When the resource extraction rate is controlled to a certain extent,the economy can achieve a stable level,environmental pollution is also reduced and resource reserves are ensured. This paper has important practical significance to realize the coordinated and sustainable development of "resource-environment-economy".
引文
1于立宏,贺媛.能源替代弹性与中国经济结构调整.中国工业经济,2013(4):30~42(Yu L H,He Y.Economic substitution elasticity and china's economic structure adjustment.China Industrial Economy,2013(4):30~42(in Chinese))
2毕宏杰,冯玉广.城市能源-经济-环境系统的Brusselator模型.系统科学学报,2013,21(4):93~96(Bi HJ,Feng Y G.Brusselator model of urban energy-economic-environment system.Journal of Systems Science,2013,21(4):93~96(in Chinese))
3陈长杰,马晓微,魏一鸣等.基于可持续发展的中国经济-资源系统协调性分析.系统工程,2004,22(3):34~39(Chen C J,Ma X W,Wei Y M,et al.Based on the sustainable development of China's economic-resource system coordination analysis.Systems Engineering,2004,22(3):34~39(in Chinese))
4吴玉鸣,张燕.中国区域经济增长与环境的耦合协调发展研究.资源科学,2008,30(1):25~30(Wu Y M,Zhang Y.Study on the coupling and coordinated development of regional economic growth and environment in china.Resources Science,2008,30(1):25~30(in Chinese))
5茹江,李彬,徐云麟等.本溪经济技术开发区环境-经济协调发展研究.环境科学,1995,16(6):47~49,72(Ru J,Li B,Xu Y L,et al.Studies on the coordinated development of environment and economy in benxi economic and technological development zone.Journal of Environmental Science,1995,16(6):47~49,72(in Chinese))
6 Hotelling H.The economic of exhaustible resources.Journal of Political Economy,1931,39(2):137~175
7 Dasgupta P,Heal G.The optimal depletion of exhaustible resources.The Review of Economic Studies,Symposium on the Economics of Exhaustible Resources.U.K.:Oxford University Press,1974,41:3~28
8 Solow R M.Intergenerational equity and exhaustible resources.Review of Economic Studies,Symposium on the Economics of Exhaustible.U.K.:Oxford University Press,1974,41:29~45
9 Stiglitz J.Growth with exhaustible natural resources:efficient and optimal growth paths.The Review of Economic Studies,Symposium on the Economics of Exhaustible Resources.U.K.:Oxford University Press,1974,41:123~137
10 Forster B A.A note on economic growth and environmental quality.The Swedish Journal of Economics,1972(6):281~85
11 Forster B A.Optimal capital accumulation in a polluted environment.Southern Economic Journal,1973(39):544~547
12张华,魏晓平.“能源-经济-环境”系统的约束与解约束:理论与实证.北京理工大学学报(社会科学版),2015,17(3):53~59(Zhang H,Wei X P.Constraints and solutions of“Energy-Economy-Environment”system:theory and empirical.Journal of Beijing Institute of Technology(Social Science Edition),2015,17(3):53~59(in Chinese))
13陈利顶,傅伯杰.长江流域可持续发展的基础与资源环境适应性评价.环境科学,1999(2):93~95(Chen LD,Fu B J.Fundamental and sustainable development of resources and environment in the yangtze river basin.Journal of Environmental Science,1999(2):93~95(in Chinese))
14王柯敬,赵艳轲.中国资源-环境-经济复合系统发展及协调状况研究:2000-2012.中央财经大学学报,2014(6):74~82(Wang K J,Zhao Y K.Research on the development and coordination of china's resources-environment-economy complex system:2000-2012.Journal of Central University of Finance and Economics,2014(6):74~82(in Chinese))
15洪开荣,浣晓旭,孙倩.中部地区资源-环境-经济-社会协调发展的定量评价与比较分析.经济地理,2013,33(12):16~23(Hong K R,Huan X X,Sun Q.Quantitative evaluation and comparative analysis of resource-environment-economy-social coordinated development in central china.Political Geography,2013,33(12):16~23(in Chinese))
16姜涛,袁建华,何林等.人口-资源-环境-经济系统分析模型体系.系统工程理论与实践,2002(12):67~72(Jiang T,Yuan J H,He L,et al.Population-ResourcesEnvironment-Economic system analysis model system.Systems Engineering Theory&Practice,2002(12):67~72(in Chinese))
17李杰兰,陈兴鹏,王雨等.基于系统动力学的青海省可持续发展评价.资源科学,2009,31(9):1624~1631(Li J L,Chen X P,Wang Y,et al.Evaluation of sustainable development in qinghai province based on system dynamics.Resources Science,2009,31(9):1624~1631(in Chinese))
18陈六君,毛潭,刘为等.环境恶化与经济衰退的动力学模型.北京师范大学学报(自然科学版),2004,40(5):617~622(Chen L J,Mao T,Liu W,et al.Environmental dynamics and economic dynamics of economic recession.Journal of Beijing Normal University(Natural Science Edition),2004,40(5):617~622(in Chinese))
19陈六君,方福康.自然资源环境系统的突变机制.复杂系统与复杂性科学,2004,1(2):1~8(Chen L J,Fang F K.Modeling mechanism of natural resources and environment system.Complex Systems and Complexity Science,2004,1(2):1~8(in Chinese))
20林子飞,徐伟,韩群.基于分数阶导数的经济波动模型的稳定性研究.动力学与控制学报,2017,15(3):242~249(Lin Z F,Xu W,Han Q.Study on the stability of economic fluctuation models based on fractional order derivatives.Journal of Dynamics and Control,2017,15(3):242~249(in Chinese))
21李佼瑞,张艳霞.带有环境净化的双随机参数SOLOW模型的稳定性.统计与信息论坛,2016(6):7~13(Li JR,Zhang Y X.Stability of dual stochastic parameters solow model with environmental purification.Journal of Statistics and Information,2016(6):7~13(in Chinese))
22王洪礼.发展中国家的环境经济模型的非线性动力学模型研究.中国力学学会一般力学专业委员会.第八届全国动力学与控制学术会议论文集.中国力学学会一般力学专业委员会,2008:1(Wang H L.Study on the nonlinear dynamics model of environmental economy model in developing countries.In:Editorial conference of the8th national conference on dynamics and control.Chinese Society of Mechanics General Mechanics Professional Committee,2008:1(in Chinese))
2毕宏杰,冯玉广.城市能源-经济-环境系统的Brusselator模型.系统科学学报,2013,21(4):93~96(Bi HJ,Feng Y G.Brusselator model of urban energy-economic-environment system.Journal of Systems Science,2013,21(4):93~96(in Chinese))
3陈长杰,马晓微,魏一鸣等.基于可持续发展的中国经济-资源系统协调性分析.系统工程,2004,22(3):34~39(Chen C J,Ma X W,Wei Y M,et al.Based on the sustainable development of China's economic-resource system coordination analysis.Systems Engineering,2004,22(3):34~39(in Chinese))
4吴玉鸣,张燕.中国区域经济增长与环境的耦合协调发展研究.资源科学,2008,30(1):25~30(Wu Y M,Zhang Y.Study on the coupling and coordinated development of regional economic growth and environment in china.Resources Science,2008,30(1):25~30(in Chinese))
5茹江,李彬,徐云麟等.本溪经济技术开发区环境-经济协调发展研究.环境科学,1995,16(6):47~49,72(Ru J,Li B,Xu Y L,et al.Studies on the coordinated development of environment and economy in benxi economic and technological development zone.Journal of Environmental Science,1995,16(6):47~49,72(in Chinese))
6 Hotelling H.The economic of exhaustible resources.Journal of Political Economy,1931,39(2):137~175
7 Dasgupta P,Heal G.The optimal depletion of exhaustible resources.The Review of Economic Studies,Symposium on the Economics of Exhaustible Resources.U.K.:Oxford University Press,1974,41:3~28
8 Solow R M.Intergenerational equity and exhaustible resources.Review of Economic Studies,Symposium on the Economics of Exhaustible.U.K.:Oxford University Press,1974,41:29~45
9 Stiglitz J.Growth with exhaustible natural resources:efficient and optimal growth paths.The Review of Economic Studies,Symposium on the Economics of Exhaustible Resources.U.K.:Oxford University Press,1974,41:123~137
10 Forster B A.A note on economic growth and environmental quality.The Swedish Journal of Economics,1972(6):281~85
11 Forster B A.Optimal capital accumulation in a polluted environment.Southern Economic Journal,1973(39):544~547
12张华,魏晓平.“能源-经济-环境”系统的约束与解约束:理论与实证.北京理工大学学报(社会科学版),2015,17(3):53~59(Zhang H,Wei X P.Constraints and solutions of“Energy-Economy-Environment”system:theory and empirical.Journal of Beijing Institute of Technology(Social Science Edition),2015,17(3):53~59(in Chinese))
13陈利顶,傅伯杰.长江流域可持续发展的基础与资源环境适应性评价.环境科学,1999(2):93~95(Chen LD,Fu B J.Fundamental and sustainable development of resources and environment in the yangtze river basin.Journal of Environmental Science,1999(2):93~95(in Chinese))
14王柯敬,赵艳轲.中国资源-环境-经济复合系统发展及协调状况研究:2000-2012.中央财经大学学报,2014(6):74~82(Wang K J,Zhao Y K.Research on the development and coordination of china's resources-environment-economy complex system:2000-2012.Journal of Central University of Finance and Economics,2014(6):74~82(in Chinese))
15洪开荣,浣晓旭,孙倩.中部地区资源-环境-经济-社会协调发展的定量评价与比较分析.经济地理,2013,33(12):16~23(Hong K R,Huan X X,Sun Q.Quantitative evaluation and comparative analysis of resource-environment-economy-social coordinated development in central china.Political Geography,2013,33(12):16~23(in Chinese))
16姜涛,袁建华,何林等.人口-资源-环境-经济系统分析模型体系.系统工程理论与实践,2002(12):67~72(Jiang T,Yuan J H,He L,et al.Population-ResourcesEnvironment-Economic system analysis model system.Systems Engineering Theory&Practice,2002(12):67~72(in Chinese))
17李杰兰,陈兴鹏,王雨等.基于系统动力学的青海省可持续发展评价.资源科学,2009,31(9):1624~1631(Li J L,Chen X P,Wang Y,et al.Evaluation of sustainable development in qinghai province based on system dynamics.Resources Science,2009,31(9):1624~1631(in Chinese))
18陈六君,毛潭,刘为等.环境恶化与经济衰退的动力学模型.北京师范大学学报(自然科学版),2004,40(5):617~622(Chen L J,Mao T,Liu W,et al.Environmental dynamics and economic dynamics of economic recession.Journal of Beijing Normal University(Natural Science Edition),2004,40(5):617~622(in Chinese))
19陈六君,方福康.自然资源环境系统的突变机制.复杂系统与复杂性科学,2004,1(2):1~8(Chen L J,Fang F K.Modeling mechanism of natural resources and environment system.Complex Systems and Complexity Science,2004,1(2):1~8(in Chinese))
20林子飞,徐伟,韩群.基于分数阶导数的经济波动模型的稳定性研究.动力学与控制学报,2017,15(3):242~249(Lin Z F,Xu W,Han Q.Study on the stability of economic fluctuation models based on fractional order derivatives.Journal of Dynamics and Control,2017,15(3):242~249(in Chinese))
21李佼瑞,张艳霞.带有环境净化的双随机参数SOLOW模型的稳定性.统计与信息论坛,2016(6):7~13(Li JR,Zhang Y X.Stability of dual stochastic parameters solow model with environmental purification.Journal of Statistics and Information,2016(6):7~13(in Chinese))
22王洪礼.发展中国家的环境经济模型的非线性动力学模型研究.中国力学学会一般力学专业委员会.第八届全国动力学与控制学术会议论文集.中国力学学会一般力学专业委员会,2008:1(Wang H L.Study on the nonlinear dynamics model of environmental economy model in developing countries.In:Editorial conference of the8th national conference on dynamics and control.Chinese Society of Mechanics General Mechanics Professional Committee,2008:1(in Chinese))
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