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Chinese Physics B 2009年第6期18卷 2168-2175页

作者：罗小华周围李锐梁亦龙罗明伟 College of Communication and Information Engineering Chongqing University of Posts and Telecom College of Biological Information Chongqing University of Posts and Telecom College of Automation Chongqing University of Posts and Telecom

Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.

关键词： Liu chaotic system Liu hyperchaotic system nonautonomous system synchronization control

THE THEOREM OF THE STABILITY OF LINEAR nonautonomous systemS UNDER THE FREQUENTLY-ACTING PERTURBATION AND ITS APPLICATION IN THE STABILITY ANALYSIS OF ROBOT

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Applied Mathematics and Mechanics(English Edition) 1991年第11期12卷 1057-1063页

作者：张书顺 Haerbin Shipbuilding Engineering Institute Haerbin

The necessary and sufficient condition of the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of[1] and [2], and the theorem of the equivalence on the uniform and asymptotical stability in the sense of Liapunov ami the stability under the frequently-acting perturbation of linear nonautonomous system has been given in this paper. Besides, the analysis of the dynamic stabilitv of robot has been presented by applying the theorem in this paper, which is closer to reality

关键词： stability nonautonomous system frequently-acting perturbation state transition matrix robot

THE THEOREM OF THE STABILITY OF NONLINEAR nonautonomous systemS UNDER THE FREQUENTLY-ACTING PERTURBATION—LIAPUNOV’S INDIRECT METHOD

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Applied Mathematics and Mechanics(English Edition) 1991年第7期12卷 717-725页

作者：张书顺商大中 Haerbin Shipbuilding Engineering Institute Haerbin

In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore, it is of significance in practice since perturbations are often not single in the time domain. Malkin proved a general theorem about thesubject. To apply the theorem, however, the user has to construct a Liapunov function which satisfies specified conditions and it is difficult to find such a function for nonlinear nonautonomous systems. In the light of the principle of Liapunov's indirect method, which is an effective method to decide the stability of nonlinear systems in the Liapunov sense, the authors have achieved several important conclusions expressed in the form of theorems to determine the stability of nonlinear nonautonomous systems under the frequently-acting perturbation.

关键词： nonautonomous system frequently-acting perturbation uniformly asymptotical stability state transition matrix

nonautonomous deformed solitons in a Bose-Einstein condensate

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Chinese Physics B 2013年第9期22卷 335-341页

作者：李泽军海文华邓艳 Department of Physics and Key Laboratory of Low-Dimensional Quantum Structure and Quantum Control of Ministry of Education Hunan Normal University

We study exact single-soliton solutions of an attractive Bose-Einstein condensate governed by a one-dimensional nonautonomous Gross-Pitaevskii system. For several different forms of time-dependent atom-atom interaction and external parabolic potential which satisfy the exact integrability scenario, we construct a set of new analytical nonautonomous deformed-soliton solutions, including the macroscopic wave function and the position of soliton＇s center of mass. The soliton characteristics are modulated by the external field parameters and deformation factors related to the number of the condensed atoms and the initial conditions. The results suggest a simple and effective method for experimentally generating matter-wave deformed solitons and manipulating their motions.

关键词： Bose-Einstein condensate nonautonomous system deformed soliton

ORBITAL STABILITY FOR SCHRDINGER systemS WITH nonautonomous COUPLED NONLINEARITIES

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Acta Mathematica Scientia 2013年第2期33卷 495-504页

作者：郭青 College of Science Minzu University of China

We prove the existence and the orbital stability of standing waves for the nonau- tonomous Schrodinger system……under suitable conditions on the coefficient functions a and b. We follow the idea of analyzing the comp... 详细信息

关键词： nonautonomous system orbital stability standing waves

ON THE EQUIVALENCE OF AUTONOMOUS AND nonautonomous DIFFERENTIAL systemS

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Annals of Differential Equations 2005年第3期21卷 529-532页

作者： Zhou Zhengxin Zhang Shanlin Dept. of Malh. Yangzhou University Yangzhou 225002

Using reflecting function of Mironenko we construct some nonautonomous differential systems which are equivalent to the given autonomous differential systems. The results are applied to discuss the existence and stabi... 详细信息

关键词： nonautonomous system reflective function equivalence periodic solution