非线性现象是现代科学最重要的研究课题之一,地理现象无不存在着非线性。目前,地理学对非线性现象的研究多从分形角度开展,对其本质——混沌的研究较少。在先前关于淮河流域洪涝变化序列及其非线性特征研究的基础上,运用混沌理论和微分方程反演理论,对淮河流域洪涝变化混沌动力系统进行了初步研究,重建了一个3维2次非线性模型。研究表明,淮河流域洪涝变化混沌动力系统具有较Lorenz等典型混沌系统更复杂的形式。
The study of the nonlinear phenomena is one of the most important fields in modern scientific research.It is called that chaos is one of the most important discoveries in the 20th century.It comes into being effect to the geographical research.As a matter of the fact, nonlinear phenomena are everywhere in geographical field.The nonlinear research in geographical filed mainly focuses on the fractal study now, especially on the geometric fractal study.However, chaos which is the basis of the nonlinear phenomena is studied less in geography.It is believed that the chaotic study will be researched gradually and successively with the deepening of the nonlinear study in geography.Based on the flood series of the Huaihe River Basin in the last 500-year period, the nonlinear phenomena of the flood series in the Huaihe River Basin, including fractal features, chaotic characteristics, attractor dimension and Lyapunov indices are previously studied.The present paper analyzes the dynamics of the flood series in the Huaihe River Basin and reconstructs a nonlinear dynamical model which is 3-dimension and second power according to chaotic theory and differential equation method.The research shows that the reconstructed nonlinear dynamical system of the flood series in the Huaihe River Basin is more complex than that of the typical chaotic model, like Lorenz model.It has reasons that the study is only beginning but useful for the nonlinear research in geography.
[1] Changnon S A.Research agenda for floods to solve policy failure[J].Water Resources Planning and Management,1985,111(1):1553-1563.
[2] 姜彤,许朋柱,高俊峰.1996年全球自然灾害分析[J].自然灾害学报,1997,6(4):14~17.
[3] 张捷,包浩生.分形理论及其在地貌学中的应用[J].地理研究,1994,13(3):105~111.
[4] 周寅康,张 捷,王腊春,等.分形论与自然灾害研究[J].自然灾害学报,1995,4(4):9~15.
[5] 中央气象局气象科学研究院(主编).中国近五百年旱涝分布图集[M].北京:地图出版社,1981.
[6] 周寅康.流域性洪涝及其指标研究[J].灾害学,1995,10(3):6~10.
[7] 周寅康,周成虎,汤其成.中国近500年流域性洪涝初步研究.南京大学学报,1996,32(2):309~315.
[8] 周寅康.淮河流域洪涝特征初步研究[J].地理研究,1996,15(1):22~29.
[9] 周寅康,包浩生,张捷.淮河流域洪涝变化吸引子维数研究.地理科学,1998,18(4):362~367.
[10] 周寅康,王腊春,张 捷.淮 河 流域洪涝变化的混沌特征[J].自然灾害学报,1999,8(1):42~47.
[11] 周寅康,付重林,王腊春,等.淮河流域洪涝变化可预报时间研究[J].自然灾害学报,1999,8(4):118~122.
[12] 周寅康,包浩生,张 捷.淮河流域洪涝变化混沌演化特征研究[J].地球信息科学,1999,2(1):7~11.
[13] 王绍武,赵宗慈.近五百年我国旱涝史料的分析[J].地理学报,1979,34(4):329~340.
[14] Zhou Yin-kang,Wang La-chun,Zhang Jie,et al.Dissipation of the flood series in the Huaihe River Basin[J].南京大学学报(Letters),1999,35(3):362-365.
[15] Tsonis A A.Chaos:from theory to applications[M].New York and London:Plenum Press,1992.
[16] Porporato A,L Ridolfi.Nonlinear analysis of river flow time sequences[J].Water Resources Research,1992,33(6),1353-1367.
[17] 黄建平,衣育红.利用观测资料反演非线性动力模型[J].中国科学(B),1991,21(3):331~336.
[18] Takens F.Detectng strange attractors in turbulence[J].Dynamical Systems and Turbulence,1981,898:366-381.
