Constructing a family of generalized Lyapunov functions,a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system.The method we proposed greatly simplifies th...Constructing a family of generalized Lyapunov functions,a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system.The method we proposed greatly simplifies the complex proofs of the two famous estimations presented by the Russian scholar Leonov.Our uniform formula can derive a series of the new estimations.Employing the idea of intersection in set theory,we extract a new Leonov formula-like estimation from the family of the estimations.With our method and the new estimation,one can confirm that there are no equilibrium,periodic solutions,almost periodic motions,wandering motions or other chaotic attractors outside the global attractive set.The Lorenz butterfly-like singular attractors are located in the global attractive set only.This result is applied to the chaos control and chaos synchronization.Some feedback control laws are obtained to guarantee that all the trajectories of the Lorenz systems track a periodic solution,or globally stabilize an unstable(or locally stable but not globally asymptotically stable)equilibrium.Further,some new global exponential chaos synchronization results are presented.Our new method and the new results are expected to be applied in real secure communication systems.展开更多
In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bo...In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bounds are derived. The results presented in this paper contain all the existing results as special cases. In particular, the critical cases, b→ 1^＋ and a→0^＋, for which the previous methods failed, have been solved using a unified formula.展开更多
Underdetermined blind signal separation （BSS） （with fewer observed mixtures than sources） is discussed. A novel searching-and-averaging method in time domain （SAMTD） is proposed. It can solve a kind of problems ...Underdetermined blind signal separation （BSS） （with fewer observed mixtures than sources） is discussed. A novel searching-and-averaging method in time domain （SAMTD） is proposed. It can solve a kind of problems that are very hard to solve by using sparse representation in frequency domain. Bypassing the disadvantages of traditional clustering （e.g., K-means or potential-function clustering）, the durative- sparsity of a speech signal in time domain is used. To recover the mixing matrix, our method deletes those samples, which are not in the same or inverse direction of the basis vectors. To recover the sources, an improved geometric approach to overcomplete ICA （Independent Component Analysis） is presented. Several speech signal experiments demonstrate the good performance of the proposed method.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.60274007,60474011)the Guangdong Povince Science Foundation for Program of Research Team(Grant No.04205783).
文摘Constructing a family of generalized Lyapunov functions,a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system.The method we proposed greatly simplifies the complex proofs of the two famous estimations presented by the Russian scholar Leonov.Our uniform formula can derive a series of the new estimations.Employing the idea of intersection in set theory,we extract a new Leonov formula-like estimation from the family of the estimations.With our method and the new estimation,one can confirm that there are no equilibrium,periodic solutions,almost periodic motions,wandering motions or other chaotic attractors outside the global attractive set.The Lorenz butterfly-like singular attractors are located in the global attractive set only.This result is applied to the chaos control and chaos synchronization.Some feedback control laws are obtained to guarantee that all the trajectories of the Lorenz systems track a periodic solution,or globally stabilize an unstable(or locally stable but not globally asymptotically stable)equilibrium.Further,some new global exponential chaos synchronization results are presented.Our new method and the new results are expected to be applied in real secure communication systems.
基金Supported partly by the National Natural Science Foundation of China (Grant Nos. 60474011 and 60274007)the National Natural Science Foun-dation of China for Excellent Youth (Grant No. 60325310)+2 种基金the Guangdong Province Science Foundation for Program of Research Team (Grant No. 04205783)the Natural Science Fund of Guangdong Province, China (Grant No. 05006508)the Natural Science and Engineering Re-search Council of Canada (Grant No. R2686A02)
文摘In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bounds are derived. The results presented in this paper contain all the existing results as special cases. In particular, the critical cases, b→ 1^＋ and a→0^＋, for which the previous methods failed, have been solved using a unified formula.
基金Supported by the National Natural Science Foundation of China (Grant Nos. U0635001, 60505005 and 60674033)the Natural Science Fund of Guangdong Province (Grant Nos. 04205783 and 05006508)the Specialized Prophasic Basic Research Projects of the Ministry of Science and Technology of China (Grant No. 2005CCA04100)
文摘Underdetermined blind signal separation （BSS） （with fewer observed mixtures than sources） is discussed. A novel searching-and-averaging method in time domain （SAMTD） is proposed. It can solve a kind of problems that are very hard to solve by using sparse representation in frequency domain. Bypassing the disadvantages of traditional clustering （e.g., K-means or potential-function clustering）, the durative- sparsity of a speech signal in time domain is used. To recover the mixing matrix, our method deletes those samples, which are not in the same or inverse direction of the basis vectors. To recover the sources, an improved geometric approach to overcomplete ICA （Independent Component Analysis） is presented. Several speech signal experiments demonstrate the good performance of the proposed method.
