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	1. Robust Hybrid Projective Synchronization of Fractional-Order Chaotic Systems with Time-Delay
	MA Tiedong,XI Quan
	Information Science and System Science 16 December 2013
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	Abstract:The hybrid projective synchronization for fractional-order chaotic systems with time-delay and uncertain perturbation is investigated in this paper. Adaptive sliding mode control method is proposed to synchronize the fractional-order chaotic and hyperchaotic systems under time-delay and uncertain perturbation. Stability is analyzed by using stability theorem of fractional calculus. The simulation results show the feasibility and effectiveness of the proposed scheme.
	TO cite this article:MA Tiedong,XI Quan. Robust Hybrid Projective Synchronization of Fractional-Order Chaotic Systems with Time-Delay[OL].[16 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4575776


	2. Circuit simulation and implementation for synchronization between fractional-order modified Liu chaotic systems
	MA Tiedong,GUO Dong
	Information Science and System Science 28 October 2013
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	Abstract:For a novel modified fractional-order Liu chaotic system, this paper studies the circuit simulation for this system and its synchronization. Based on the approximation theory of fractional-order operator, an electronic circuit is designed to describe the dynamic behavior of the modified fractional-order system firstly, and then the synchronization between two identical fractional-order Liu systems is designed by given circuit. Our results are supported by numerical simulation and circuit implementation.
	TO cite this article:MA Tiedong,GUO Dong. Circuit simulation and implementation for synchronization between fractional-order modified Liu chaotic systems[OL].[28 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4565866


	3. A new multistage chaos synchronized system for secure communications
	AN Xinlei,Yu JianNing,Zhang JianGang,ZHANG Li
	Information Science and System Science 12 March 2009
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	Abstract:Based on Lyapunov stabilization theorem, considering the diffusionless chaotic system, a method is proposed for global chaos synchronization among three identical systems. Meanwhile, the method of three different structures chaotic systems global synchronization is shown. Then this method is applied to secure communication through chaotic masking, used three coupled identical system, propose a novel method of chaos encryption, after encrypting in the first two coupled systems, do it again in the later two coupled systems. Simulation results show that the method can realize monotonous synchronization. Further more, the information signal can be recovered undistorted when applying this method to secure communication.
	TO cite this article:AN Xinlei,Yu JianNing,Zhang JianGang, et al. A new multistage chaos synchronized system for secure communications[OL].[12 March 2009] http://en.paper.edu.cn/en_releasepaper/content/30178


	4. 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


	5. 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].

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