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复合系统的混沌性
Chaos in the Compositional Systems

吴新星*,朱培勇
WU Xinxing,ZHU Peiyong

电子科技大学数学科学学院, 成都, 四川, 611731
School of Mathematics, University of ElectronicScience and Technology of China, Chengdu, Sichuan, 611731,P. R. China

收稿日期: 2011-01-18
出版日期: 2013-06-25
DOI: 10.11845/sxjz.2011005b

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摘要 本文讨论复合系统混沌性与原系统混沌性之间的联系. 首先证明:在紧度量空间上, 所有的复合系统都保持原系统的Li-Yorke混沌性, 并且用反例说明, 在一般的度量空间, 该结论不成立. 其次, 研究复合系统的分布混沌性, 得到和Li-Yorke混沌相似的结论. 最后, 用实例说明:对于任意的正整数$n\geq 2$, 存在紧致Devaney混沌系统, 其$n$次复合系统却不是Devaney混沌的.
关键词 Li-Yorke混沌分布混沌Devaney混沌初值敏感依赖    
Abstract:This paper isdevoted to studying the relations between the chaoticity ofcompositional systems and primary systems. First, it is proved thaton a compact metric space, all the compositional systems preserveLi-Yorkes chaoticity of the primary systems. And a counterexampleis given to show that on a general metric space, this conclusiondoes not hold. Next, we study the distributional chaoticity ofcompositional systems and obtain some conclusions which are similarto Li-Yorke chaos. Finally, we use an example to show that for any$n\geq 2$, there exists a compact system which is chaotic in the senseof Devaney, but its $n$th compositional system is not.
Key wordsdistributional chaos    Devaneychaos    sensitive dependence on initial conditions
基金资助:国家自然科学基金(No. 10671134)和四川省教育厅科研基金(No. 12ZA098)
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