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	1. Star direct product of symbolized vertex shift matrices: angle decomposition method in symbolic dynamics
	Xu Chuanyun ,Peng Shouli ,Cao Kefei
	Information Science and System Science 09 February 2009
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	Abstract:A star direct product in the form of matrices is proposed for one-dimensional symbolic dynamics of arbitrary multimodal maps. The direct product is based on the angle decomposition technique in the from of symbolized vertex shift matrices which are orthonormal 0-1 matrices and form a special orthonormal group. The admissibility condition of symbolized vertex shift matrices and the admissibility of star direct product are proved in detail. They will guarantee that the product are of renormalizable orbits. The star direct product has many algebraic distinctions to the conventional star product. Therefore, it is expected that there may exist a great diversity of Feigenbaum\\\
	TO cite this article:Xu Chuanyun ,Peng Shouli ,Cao Kefei . Star direct product of symbolized vertex shift matrices: angle decomposition method in symbolic dynamics[OL].[ 9 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28636


	2. Universal Form of Renormalizable Knots in Symbolic Dynamics of Bimodal Maps
	Wen Gao,Chuan-Yun Xu,Shou-Li Peng,Ke-Fei Cao
	Information Science and System Science 22 January 2009
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	Abstract:The universal relation between knot theory and symbolic dynamics is established in bimodal maps in this paper. When symbolic sequences of maps are expressed as simple knots, it is easy to find that knots for renormalizable sequences are constructed of bunches of flows. They are parallel, inverse parallel or single-folding. The generation of renormalizable knots can be operated easily in geometry or be calculated by algebraic method. Especially, it is independent of traditional star product of symbolic dynamics. We present some examples and list them in a table with period not beyond 6.
	TO cite this article:Wen Gao,Chuan-Yun Xu,Shou-Li Peng, et al. Universal Form of Renormalizable Knots in Symbolic Dynamics of Bimodal Maps[J].


	3. Generation & Analysis on a Novel Autonomous Chaotic System with Manifold Variable Lyapunov Exponents
	Tang Binhua ,He Li ,Yang Zhi
	Information Science and System Science 10 May 2006
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	Abstract:A high-dimension chaotic system based on Multivariable Linkage Function (MvLF) is proposed within the passage, which has variable Lyapunov exponents (LEs) and the sufficient capabilities to implement different chaotic, hyperchaotic status, or both. Not only does it have much more security than the former similar ones, but its expansibility and physical simplicity in modeling and applications also excel others. The passage carried out relevant analysis on the eigenvalue problem of system Jacobian matrix and their Lyapunov exponent spectrum, which finally led to two general conclusions for the cases under investigation. Relevant simulations and analysis prove that the proposed system has theoretical importance and practical advantages in information security domain, such as chaotic communication, modern chaotic cryptology, etc.
	TO cite this article:Tang Binhua ,He Li ,Yang Zhi . Generation & Analysis on a Novel Autonomous Chaotic System with Manifold Variable Lyapunov Exponents[OL].[10 May 2006] http://en.paper.edu.cn/en_releasepaper/content/6547


	4. A Constructive Generalized Synchronization Theorem for Array Differential Equations with Application to Secure Image Communication
	Min Lequan,Zang hongyan
	Information Science and System Science 02 March 2005
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	Abstract: A constructive theorem of generalized synchronization (GS) for unidirectionally coupled array differential equations (ADE) is presented. Based on the theorem, one can design a GS driven ADE via a driving chaotic ADE and a C^1 diffeomorphism. As an application, a smoothed Chua
	TO cite this article:Min Lequan,Zang hongyan. A Constructive Generalized Synchronization Theorem for Array Differential Equations with Application to Secure Image Communication[OL].[ 2 March 2005] http://en.paper.edu.cn/en_releasepaper/content/1620

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