[1]王福来,达庆利.广义Lorenz映射的混沌行为及不变密度[J].东南大学学报(自然科学版),2007,37(4):711-715.[doi:10.3969/j.issn.1001-0505.2007.04.033]
 Wang Fulai,Da Qingli.Chaotic behavior of generalized Lorenz maps and its invariant density[J].Journal of Southeast University (Natural Science Edition),2007,37(4):711-715.[doi:10.3969/j.issn.1001-0505.2007.04.033]
点击复制

广义Lorenz映射的混沌行为及不变密度()
分享到:

《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
37
期数:
2007年第4期
页码:
711-715
栏目:
经济与管理
出版日期:
2007-07-20

文章信息/Info

Title:
Chaotic behavior of generalized Lorenz maps and its invariant density
作者:
王福来12 达庆利1
1 东南大学经济管理学院,南京 210096; 2 浙江财经学院数学与统计学院, 杭州 310012
Author(s):
Wang Fulai12 Da Qingli1
1 School of Economics and Management, Southeast University, Nanjing 210096, China
2 School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310012, China
关键词:
广义Lorenz映射 符号动力系统 混沌 拓扑熵 不变密度
Keywords:
generalized Lorenz maps symbolic dynamics chaos topological entropy invariant density
分类号:
N941.7;O177.99
DOI:
10.3969/j.issn.1001-0505.2007.04.033
摘要:
用符号动力学证明了广义的、即具有2个或以上间断点的分段线性Lorenz映射以移位自同构为子系统,即系统是混沌的,并给出了拓扑熵的下界以及Lyapunov指数的上界与下界.讨论了广义Lorenz映射的不稳定周期轨道的周期及稠密性,给出了不稳定周期轨道的周期.用构造下界函数的方法论证了分段线性广义Lorenz映射在随机作用随机扰动下系统具有统计稳定性.
Abstract:
Proof is given to the conclusion that a subset of symbolic system is shift automorphic to a family of generalized and piecewise continuous Lorenz maps, which means that the generalized Lorenz map is chaotic. There are two or more points of discontinuity in the Lorenz maps which are linear on every sub-interval. The unstable periodic and dense orbits are discovered and hence periods are given. Lower bounds of the maps are given and both lower and upper bounds for the local Lyapunov exponent are also given. At last it is proved that, by constructing a lower bound function, the family of generalized Lorenz maps have invariant density under stochastic perturbations.

参考文献/References:

[1] Percival I,Vivaldi F.Arithmetical properties of strongly chaotic motions[J]. Physica D,1987,25(1):105-130.
[2] 王福来.广义Taylor映射与Henon映射具有混沌条件的改进[J].数学进展,2004,33(5):591-597.
  Wang Fulai.An improvement on the conditions of generalized Taylor map and Henon map containing chaos[J].Advances in Mathematics,2004,33(5):591-597.(in Chinese)
[3] Lasota A,Mackey M. Chaos,fractals and noise[M].2nd ed.New York:Springer-Verlag,1994.
[4] 丁义明,范文涛.一簇Lorenz映射的混沌行为与统计稳定性[J].数学物理学报,2001,21A(4):559-569.
  Ding Yiming,Fan Wentao.The chaotic behavior and statistically stable behavior of a family of Lorenz maps[J].Acta Math Sci,2001,21A(4):559-569.(in Chinese)
[5] Keener J.Chaotic behavior in piecewise continuous difference equations[J]. Trans Amer Mat Soc,1980,26(1):589-604.
[6] Malkin M L.Rotation intervals and the dynamics of Lorenz type mappings[J]. Selecta Mahematica Sovietica,1991,2(10):265-275.
[7] Ding Yiming,Fan Wentao.Asymptotic periodicity of Lorenz maps[J].Acta Math Sci,1999,19(1):114-120.
[8] 郑伟谋,郝柏林.实用符号动力学[M].上海:上海科技教育出版社,1994:11.
[9] 闵琦,陈中轩.洛伦兹映射拓扑熵计算的一点技巧[J].云南大学学报,2001,23(1):24-26.
  Min Qi,Chen Zhongxuan.The skills on calculating topological entropy of Lorenz maps[J]. Journal of Yunnan University Engineering Science,2001,23(1):24-26.(in Chinese)
[10] Elezovic N,Zupanovic V,Zubrinic D.Box dimension of trajectories of some discrete dynamical systems[J].Chaos,Solitons & Fractals,2007,34(2):244-252.
[11] Chen Z X,Cao K F,Peng S L.Symbolic dynamics analysis of topological entropy and its multifractal structure[J].Phys Rev E,1995,51(3):1983-1988.

备注/Memo

备注/Memo:
作者简介: 王福来(1970—),男,博士生; 达庆利(联系人),男,教授,博士生导师, dql@public1.ptt.js.cn.
更新日期/Last Update: 2007-07-20