Journal of Guangxi Normal University(Natural Science Edition) ›› 2012, Vol. 30 ›› Issue (4): 1-12.

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Study of the Lorenz Equations in a New Parameter Space

LIU Jun-xian1, PEI Qi-ming2, QIN Zong-ding1, JIANG Yu-ling1   

  1. 1.College of Physics and Technology,Guangxi Normal University,Guilin Guangxi 541004,China;
    2.School of Physical Science and Technology,Yangtze University,Jingzhou Hubei 434023,China
  • Received:2012-05-25 Published:2018-11-27

Abstract: The system of Lorenz equations is investigated in anew parameter space which is constructed through linear stability analysis.Many new interesting phenomena are found,for example,there are abundant co-existences,such as,theco-existences of the fixed points and a periodic or chaotic attractor,and theco-existences of aperiodic orbit and a sequence of period-doubling bifurcation to chaos.The system also exhibits some properties of an unimodal map at certain area of the new parameter space,and the related U-sequence exists.

Key words: Lorenz equations, bifurcation, chaos, U-sequence

CLC Number: 

  • O415.5
[1] GLEICK J.混沌学传奇[M].卢侃,孙建华,译.上海:上海翻译出版公司,1991.
[2] SPARROW C.The lorenz equation:bifurcations,chaos and strange attractors[M].New York:Springer-Verlag,1982.
[3] VISWANATH D.Symbolic dynamics and periodic orbits of the Lorenz attractor[J].Nonlinearity,2003,16(3):1035-1056.
[4] 裴启明,刘军贤.一种新混沌系统的动力学行为及符号序列排序规则[J].广西师范大学学报:自然科学版,2009,27(4):1-6.
[5] 陈关荣.广义Lorenz系统及其规范式[C]//第七届全国非线性动力学学术会议和第九届全国非线性振动学术会议论文集.南京:中国振动工程学会,2004:37-44.
[6] 何文平,封国林,高新全,等.准周期外力驱动下Lorenz系统的动力学行为[J].物理学报,2006,55(6):3175-3179.
[7] 侯威,封国候,董文杰.基于复杂度分析logistic映射和Lorenz模型的研究[J].物理学报,2005,54(8):3940-3946.
[8] VISWANATH D.The fractal property of the Lorenz attractor[J].Physica D,2004,190(1/2):115-128.
[9] GRIGORENKO I,GRIGORENKO E.Chaotic dynamics of the fractional Lorenz system[J].Physics Review Letters,2003,91(3):034101.
[10] LÜ Jin-hu,CHEN Guan-rong,YUYong-guang.Asymptotic analysis of a modified Lorenz system[J].Chinese Physics Letters,2002,19(9):1260-1263.
[11] 刘孝贤,刘晨.Lorenz系统的动力学特性及对称特性[J].山东工业大学学报,1998,28(5):501-508.
[12] VAKAKIS A F,AZEEZ M F A.Analytic approximation of the homoclinic orbits of the Lorenz system at σ=10,b=8/3 and ρ=13.926…[J].Nonlinear Dynamics,1998,15(3):245-257.
[13] CHOE Chol-ung,HO··HNE K,BennerH,et al.Chaos suppression in the parametrically driven Lorenz system[J].Physical Review E,2005,72(3):036206.
[14] 宁娣,陆君安.一个临界系统与Lorenz系统和Chen系统的异结构同步[J].物理学报,2005,54(10):4590-4595.
[15] PARK E H,ZAKS M A,KURTHS J.Phase synchronization in the forcedLorenz system[J].Physical Review E,1999,60(6):6627-6638.
[16] TOMITA K,TSUDA I.Towards the interpretation of the global bifurcation structure of the Lorenz system:a simple one-dimensional model[J].Progress of Theoretical Physics Supplement,1980(69):185-199.
[17] FANG Hai-ping,HAO Bai-lin.Symbolic dynamics of the Lorenz equations[J].Chaos,Solitons and Fractals,1996,7(2):217-246.
[18] RASBAND N S.Chaotic dynamics of nonlinear systems[M].New York,USA:A Wiley-Interscience Publication,1989.
[19] 刘秉正,彭建华.非线性动力学[M].北京:高等教育出版社,2005.
[20] HAO Bai-lin,LIU Jun-xian,ZHENG Wei-mou.Symbolic dynamicsanalysis of the Lorenz equations[J].Physical Review E,1998,57(5):5378-5396.
[21] 刘军贤.常微分方程的符号动力学[D].北京:中国科学院理论物理研究所,1996.
[22] LIU Jun-xian,ZHENG Wei-mou,HAO Bai-lin.From annular to interval dynamics:symbolic analysis of the periodically forced Brusselator[J].Chaos,Solitons and Fractals,1996,7(9):1427-1453.
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