A centrosymmetric chaos

Symmetry plays an important part in the research of the dynamical behavior of nonlinear system. It is proved in this paper that, for a class of centrosymmetric systems with parametric excitation, chaos behaves in centrosymmetric manner, which implies that chaos need not to be an unsymmetric dynamical state. The project supported by National Natural Science Foundation of China     

Steady state motions of shallow arch under periodic force with 1∶2 internal resonance on the plane of physical parameters

The bifurcation dynamics of shallow arch which possesses initial deflection under periodic excitation for the case of 1∶2 internal resonance is studied in this paper. The whole parametric plane is divided into several different regions according to the types of motions; then the distribution of steady state motions of shallow arch on the plane of physical parameters is obtained. Combining with numerical method, the dynamics of the system in different regions, especially in the Hopf bifurcation region, is studied in detail. The rule of the mode interaction and the route to chaos of the system is also analysed at the end. Project supported by National Natural Science Foundation and National Youth Science Foundation of China     

Application of wavelet transform to bifuraation and chaos study

The response of a nonlinear vibration system may be of three types, namely, periodic, quasiperiodic or chaotic, when the parameters of the system are changed. The periodic motions can be identified by Poincare map, and harmonic wavelet transform (HWT) can distinguish quasiperiod from chaos, so the existing domains of different types of motions of the system can be revealed in the parametric space with the method of HWT joining with Poincar'e map. Communicated Zhang Ruqing Project supported by the National Natural Science Foundation of China     

Analysis of global dynamics in a parametrically excited thin plate

The global bifurcations and chaos of a simply supported rectangular thin plate with parametric excitation are analyzed. The formulas of the thin plate are derived by von Karman type equation and Galerkin's approach. The method of multiple scales is used to obtain the averaged equations. Based on the averaged equations, the theory of the normal form is used to give the explicit expressions of the normal form associated with a double zero and a pair of pure imaginary eigenvalues by Maple program. On the basis of the normal form, a global bifurcation analysis of the parametrically excited rectangular thin plate is given by the global perturbation method developed by Kovacic and Wiggins. The chaotic motion of thin plate is also found by numerical simulation. The project supported by the National Natural Science Foundation of China (10072004) and by the Natural Science Foundation of Beijing (3992004)     

Bifurcation in a parametrically excited two-degree-of-freedom nonlinear oscillating system with 1∶2 internal resonance

The nonlinear response of a two-degree-of-freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first-order autonomous ordinary differential equations for the modulation of the amplitudes and phases. The steadystate solutions of the modulated equations and their stability are investigated. The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos. Project supported by the National Natural Science Foundation of China (19472046)     

Finite-time chaos control of unified chaotic systems with uncertain parameters

This paper is concerned with finite-time chaos control of unified chaotic systems with uncertain parameters. Based on the finite-time stability theory in the cascade-connected system, a nonlinear control law is presented to achieve finite-time chaos control. The controller is simple and easy to be constructed. Simulation results for Lorenz, Lü, and Chen chaotic systems are provided to illustrate the effectiveness of the proposed scheme. Supported by the National Natural Science Foundation of China (Grant No. 60674024).     

The global bifurcation and chaos for the coupling between longitudinal and transverse vibration of a thin elastic plate in large overall motion

This paper presents the global bifurcation and chaotic behavior for the coupling of longitudinal and transverse vibration of a thin elastic plate in large overall motion. First the parametric equations of the homoclinic orbits of such a system is obtained. Then, by using the Melnikov method and digital computer simulation. the behavior of bifurcation and chaos of this vibration system is investigated in the cases of different resonances. The obvious difference between the transverse vibration and the coupling of transverse and longitudinal vibration is also shown.The project supported by the National Natural Science Foundation of China.     

连续动力学系统中混沌的参数开闭环控制

针对可能呈现混沌性态的连续动力学，提出了一种参数开闭环控制方案。以控制Ｌｏｒｅｎｚ混沌为例说明该方案的应用。讨论了参数开闭环控制与输送控制、参数输送控制及开闭环控制之间的关系。     

Dynamical Behavior of Viscoelastic Cylindrical Shells Under Axial Pressures

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｏｒｙｏｆｖｉｓｃｏｅｌａｓｔｉｃｉｔｙａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎｓｈａｖｅｂｅｅｎｂｅｃｏｍｉｎｇａｖｅｒｙａｔｔｒａｃｔｉｖｅｒｅｓｅａｒｃｈｆｉｅｌｄｓｉｎｃｅｖｉｓｃｏｅｌａｓｔｉｃｓｔｒｕｃｔｕｒｅｓｗｅｒｅｗｉｄｅｌｙａｐｐｌｉｅｄｉｎｔｏｖａｒｉｏｕｓｅｎｇｉｎｅｅｒｉｎｇ .Ｂｕｔｔｏｔｈｅａｕｔｈｏｒｓ’ｋｎｏｗｌｅｄｇｅ,ｔｈｅｒｅａｒｅｒａｒｅｆｏｒｐａｐｅｒｓｃｏｎｃｅｒｎｉｎｇｗｉｔｈｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｏｆｖｉｓｃｏｅ…     

The resonances of parametric vibration with forced vibration of the stator system of hydroelectric-generator stimulated by electromagnetism

The resonances of parametric vibration with forced vibration is analyzed, the bifurcation equation of the system is obtained and the singularity analysis is made. Some of the laws and phenomena are revealed. The transition variety and bifurcation diagram of the physical parametric plane are given. The results can be used in engineering. Supported by National Natural Science Foundation and Doctoral Programme Foundation of Institution of Higher Education of China.     

THEORY AND ALGORITHM OF OPTIMAL CONTROL SOLUTION TO DYNAMIC SYSTEM PARAMETERS IDENTIFICATION (Ⅱ) ──STOCHASTIC SYSTEM PARAMETERS IDENTIFICATION AND APPLICATION EXAMPLE

Based on the contents Of part (Ⅰ) and stochastic optimal control theory, the concept of optimal control solution to parameters identification of stochastic dynamic system is discussed at first. For the completeness of the theory developed in this paper and part (Ⅰ), then the procedure of establishing HamiltonJacobi-Bellman (HJB) equations of parameters identification problem is presented.And then, parameters identification algorithm of stochastic dynamic system is introduced. At last, an application example-local nonlinear parameters identification of dynamic system is presented.     

ROBUST CONTROL OF PERIODIC BIFURCATION SOLUTIONS

The topological bifurcation diagrams and the coefficients of bifurcation equation were obtained by C-L method. According to obtained bifurcation diagrams and combining control theory, the method of robust control of periodic bifurcation was presented, which differs from generic methods of bifurcation control. It can make the existing motion pattern into the goal motion pattern. Because the method does not make strict requirement about parametric values of the controller, it is convenient to design and make it. Numerical simulations verify validity of the method.     

混沌Mathieu_Duffing振子的开闭环控制

By using the idea of open-plus-closed-loop（OPCL） control, a controller composed of an external excitation and a linear feedback is designed to entrain chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits. The global basin of entrainment of this open-plus-closed-loop control is proved by combining the Lyapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations. Numerical simulations are performed to verify the theoretical results.     

Limited-view optical tomography technique and its application to temperature field measurement in flow of hot air

In this paper, a limited-view optical tomography technique is presented, which contains an orthographic holography system, an image processing system and the simultaneous algebraic reconstruction technique (SART). Using this technique, the temperature field of a cross section in the flow of hot air from a nozzle is measured. The measured results are satisfactory. The project supported by the National Natural Science Foundation and the State Science and Technology Commission of China     

THEORY AND METHOD OF OPTIMAL CONTROL SOLUTION TO DYNAMIC SYSTEM PARAMETERS IDENTIFICATION (I)──FUNDAMENTAL CONCEPT AND DETERMINISTIC SYSTEM PARAMETERS IDENTIFICATION

Based on the concept of optimal control solution to dynamic system parameters identification and the optimal control theory of deterministic system, dynamics system parameters identification problem is brought into correspondence with optimal control problem. Then the theory and algorithm of optimal control are introduced into the study of dynamic system parameters identification. According to the theory of Hamilton-Jacobi-Bellman (HJB) equations' solution, the existence and uniqueness of optimal control solution to dynamic system parameters identification are resolved in this paper. At last the parameters identification algorithm of determi-nistic dynamic system is presented also based on above mentioned theory and concept. Project supported by the National, Defence Science and Technology Foundation (A966000-50) and the Across Century Scientist Foundation from the State Education Commission of China     

Convective coupled map for simulating spatiotemporal chaos in flows

A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid flows. It is found that the parameter region of spatiotemporal chaos can be determined by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for turbulence such that the route to spatiotemporal chaos in fluid flows can be envisaged. The study is supported by “Nonlinear Sciences Project” from the State Science and Technology Commission of China.     

On the Homoclinic Orbits in a Class of Two-Degree-of-Freedom Systems under the Resonance Conditions

ＩｎｔｒｏｄｕｃｔｉｏｎＴｗｏ＿ｄｅｇｒｅｅ＿ｏｆ＿ｆｒｅｅｄｏｍｓｙｓｔｅｍｓｈａｖｉｎｇｃｕｂｉｃｎｏｎｌｉｎｅａｒｉｔｉｅｓａｒｅｅｘｔｅｎｓｉｖｅｌｙｕｓｅｄｉｎｐｈｙｓｉｃｓ,ｍｅｃｈａｎｉｃｓ.Ｆｏｒｅｘａｍｐｌｅ :ｔｈｅｌａｒｇｅ＿ａｍｐｌｉｔｕｄｅｖｉｂｒａｔｉｏｎｓｏｆｓｔｒｉｎｇｓ,ｂｅａｍｓ,ｍｅｍｂｒａｎｅｓａｎｄｐｌａｔｅｓ ,ｄｙｎａｍｉｃｖｉｂｒａｔｉｏｎ＿ｉｓｏｌａｔｉｏｎｓｙｓｔｅｍｓ ,ｄｙｎａｍｉｃｖｉｂｒａｔｉｏｎａｂｓｏｒｂｅｒｓ,ｔｈｅｍｏｔｉｏｎｏｆｓｐｈｅ…     

Parametric equations of nonholonomic nonconservative systems in the event space and the method of their integration

In this paper, the parametric equations with multipliers of nonholonomic nonconservative systems in the event space are established, their properties are studied, and their explicit formulation is obtained. And then the field method for integrating these equations is given. Finally, an example illustrating the application of the integration method is given. The Project is supported by the National Natural Science Foundation of China.