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【期刊论文】Introduction to anti-control of discrete chaos: theory and applications
史玉明, BY GUANRONG CHEN, * AND YUMING SHI
Phil. Trans. R. Soc. A(2006)364, 2433-2447,-0001,():
-1年11月30日
In this paper, the notion of anti-control of chaos (or chaotification) is introduced, which means to make an originally non-chaotic dynamical system chaotic or enhance the existing chaos of a chaotic system. The main interest in this paper is to employ the classical feedback control techniques. Only the discrete case is discussed in detail, including both finite-dimensional and infinite-dimensional settings.
chaos, chaotification, finite-and infinite-dimensional discrete chaos
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【期刊论文】Study on chaos induced by turbulent maps in noncompact sets☆
史玉明, Yuming Shi a, b, *, Pei Yu b
Chaos, Solitons and Fractals 28(2006)1165-1180,-0001,():
-1年11月30日
This paper is concerned with chaos induced by strictly turbulent maps in noncompact sets of complete metric spaces. Two criteria of chaos for such types of maps are established, and then a criterion of chaos, characterized by snap-back repellers in complete metric spaces, is obtained. All the maps presented in this paper are proved to be chaotic either in the sense of both Li-Yorke and Wiggins or in the sense of both Li-Yorke and Devaney. The results weaken the assumptions in some existing criteria of chaos. Several illustrative examples are provided with computer simulation.
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【期刊论文】Stability and chaos in 2-D discrete systems☆
史玉明, Guanrong Chen a, *, Chuanjun Tian b, Yuming Shi c
Chaos, Solitons and Fractals 25(2005)637-647,-0001,():
-1年11月30日
This paper is concerned with 2-D discrete systems of the form xm-1, n=f(xm,n, xm,n+1), where f:R2→R is a function, m, n e N0={0, 1, 2, . . .}. Some sufficient conditions for this system to be stable and a verification of this system to be chaotic in the sense of Devaney, respectively, are derived.
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【期刊论文】CHAOTIFICATION OF DISCRETE DYNAMICAL SYSTEMS GOVERNED BY CONTINUOUS MAPS*
史玉明, YUMING SHI, GUANRONG CHEN
International Journal of Bifurcation and Chaos, Vol. 15, No.2(2005)547-555,-0001,():
-1年11月30日
This paper is concerned with chaoti cation of discrete dynamical systems in nite-dimensional real spaces, via feedback control techniques. A chaoti cation theorem for one-dimensional discrete dynamical systems and a chaoti cation theorem for general higher-dimensional discrete dynamical systems are established, respectively. The controlled systems are proved to be chaotic in the sense of Devaney. In particular, the maps corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions on two very small disjoint closed subsets in the domains of interest. This condition is weaker than those in the existing relevant literature.
Chaos, chaoti cation, feedback control, discrete dynamical system
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史玉明, 史玉明*, *, 陈关荣
中国科学A辑数学2004, 34(5):595~609,-0001,():
-1年11月30日
研究Banachl空间上连续Frechet可微映射导出的离散动力系统之混沌。建立一个由正则非退化同宿轨道产生混沌的判定定理,并对n维实空间上的离散动力系统的混沌进行了讨论,建立了两个由非退化返回扩张不动点产生混沌的判定定理,其中一个为Marotto定理的修正定理。特别地,分别给出了一般Banach空间及n维实空间上的连续可微映射不动点为扩张的充分必要条件,彻底解决了多年以来人们对n维实空间上连续可微映射不动点的扩张性与其Jacobi矩阵特征值之间关系的困惑。
混沌, 离散动力系统, Banach空间, Marotto定理
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