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麻烦帮忙给查一篇文章的Sci检索号（UT ISI），我们这里没有这个数据库Estimating the ultimate bound and positively invariant set for a new chaotic system and its application in chaos synchronization 先谢谢啦。 |
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2楼2010-04-15 09:34:10
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小木虫(金币+0.5):给个红包，谢谢回帖交流
小木虫(金币+0.5):给个红包，谢谢回帖交流
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stimating the ultimate bound and positively invariant set for a new chaotic system and its application in chaos synchronization 作者: Shu YL (Shu, Yonglu)1, Xu HX (Xu, Hongxing)1, Zhao YH (Zhao, Yunhong)1 来源出版物: CHAOS SOLITONS & FRACTALS 卷: 42 期: 5 页: 2852-2857 出版年: DEC 15 2009 被引频次: 0 参考文献: 28 引证关系图 摘要: In this paper, we investigate the ultimate bound and positively invariant set for a new chaotic system via the generalized Lyapunov function theory. For this system, we derive a three-dimensional ellipsoidal ultimate bound and positively invariant set. In addition, the two-dimensional bound with respect to x - z and y - z are established. Finally, the result is applied to the study of completely chaos synchronization, an exact threshold is given with the system parameters. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme. (C) 2009 Elsevier Ltd. All rights reserved. 文献类型: Article 语言: English KeyWords Plus: LORENZ-SYSTEM; CHEN SYSTEM; ATTRACTOR; TRAJECTORIES; EQUATION; CIRCUIT; FAMILY 通讯作者地址: Xu, HX (通讯作者), Chongqing Univ, Coll Math & Phys, Chongqing 400044, Peoples R China 地址: 1. Chongqing Univ, Coll Math & Phys, Chongqing 400044, Peoples R China 电子邮件地址: xhx020211@sina.com 基金资助致谢: 基金资助机构 授权号 National Nature Youth Foundation of China 10601071 [显示基金资助信息] Project supported by the Foundation item the National Nature Youth Foundation of China (No. 10601071). 出版商: PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND 学科类别: Mathematics, Interdisciplinary Applications; Physics, Multidisciplinary; Physics, Mathematical IDS 号: 489MW ISSN: 0960-0779 DOI: 10.1016/j.chaos.2009.04.003 |
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4楼2010-04-15 09:52:58
深海幽蓝
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Estimating the ultimate bound and positively invariant set for a new chaotic system and its application in chaos synchronization Yonglu Shua, Hongxing Xu, a, and Yunhong Zhaoa aCollege of Mathematics and Physics, Chongqing University, Chongqing 400044, China Accepted 1 April 2009. Available online 1 May 2009. Abstract In this paper, we investigate the ultimate bound and positively invariant set for a new chaotic system via the generalized Lyapunov function theory. For this system, we derive a three-dimensional ellipsoidal ultimate bound and positively invariant set. In addition, the two-dimensional bound with respect to x-z and y-z are established. Finally, the result is applied to the study of completely chaos synchronization, an exact threshold is given with the system parameters. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme. Article Outline 1. Introduction 2. The ultimate bound and positive invariant set of this new chaotic system 3. Estimate of the two-dimensional bound with respect to y-z and x-z 4. The application in chaos synchronization 5. Simulation studies 6. Conclusions References 1. Introduction Since Lorenz discovered the well-known Lorenz chaotic system [1], many other chaotic systems have been found, including the well-known Rössler system [2], Chua’s circuit [3], which have been served as models for the study of chaos. In late 1990s, a new chaotic system was found, which is dual to the Lorenz system, and it is called the Chen system [4]. Due to its close relation to the Lorenz system, it has been widely studied [5], [6] and [7]. In the new century, many new simple chaotic systems were found: Lü system [8], unified system [9], and Lorenz-like system [10] to just name a few examples. The ultimate bound of a system is important for the study of the qualitative behavior of a chaotic system [11] and [12]. If we can show that a system under consideration has a globally attractive set, then we know that the system cannot have equilibrium points, periodic solutions, quasi-periodic solutions, or other chaotic attractors outside the globally attractive set. This greatly simplifies the analysis of the dynamical properties of the system. The ultimate bound also plays an important role in designing scheme for chaos control and chaos synchronization. The ultimate bound property of the Lorenz system has been investigated by many researchers. From1985 to 1987, Leonov gave the original results of globally ultimate bound of the Lorenz system [13], [14] and [15]. Then, Swinnerton-Dyer showed that Lyapunov function can be used to study the bounds for trajectories of the Lorenz equations [16]. This idea was further developed by Liao X et al. to get new globally attractive set and positively invariant set of the Lorenz system by constructing a family of generalized Lyapunov functions, and this result was applied to study of chaos control and chaos synchronization [17]. By using the same method, Li et al. filled the gap of estimating the ultimate bound of the Lorenz system for 0 However, the ultimate bounds of many other chaotic system remain to be solved. Sun [22] got an ultimate bound of a generalized Lorenz system. Li et al. [18] and [19] got an ultimate bound for the unified chaotic system for 0α<1/29. Qin and Chen investigated the ultimate bound of Chen system in [23], but the parameter values considered does not cover the most interesting case of the Chen’s chaotic attractor [4]. Yu and Liao showed that there exists exponential attractive set for a general chaotic system which does not belong to the known Lorenz system, or the Chen system, or the Lorenz family [24]. The estimation of the ultimate bound for the smooth Chua’s system was given in [25]. And recently an ultimate bound and positively invariant set for the hyperchaotic Lorenz–Haken system was obtained in [26]. Recently, Chu and Li [27] introduced the following new system: (1)where (a,b,c)R3 is a vector parameter. System (1) displays a typical chaotic attractor when a=5,b=16,c=1 (see Fig. 1). Some basic dynamical properties are studied in [27]. But many properties of this new system remain to be further uncovered. In this paper, we first investigate the ultimate bound and positively invariant set for this new chaotic system using the generalized Lyapunov function theory, and then we study the synchronization of this system. By employing a linear feedback controller with a single variable, an exact threshold is given with the system parameters based on the ultimate bound of what we get. As the scheme is simple, it is easy to implement in practical applications. |
5楼2010-04-15 12:38:11
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