This paper surveys recent advances in the study on the stability and bifurcation of time-delay systems. The review focuses mainly on the achievements of authors' team in the fundamental studies of stability, Hopf bifurcation and utilization of time delays to improve the system stability, as well as the delay effects on the stability of some typical systems or structures, including an aircraft wing, an inverted double-pendulum and networks. Finally, the paper addresses some open problems for future investigations.

The response prediction and stability analysis are always hot topics of research in stochastic dynamics. Developing the method for response prediction of nonlinear stochastic systems and determining the qualitative behavior of the system response are of important significance and extensive application potential. This paper reviews response and stability of multi-degree-of-freedom nonlinear stochastic systems. Firstly, main methods for the response prediction of stochastic systems are outlined, such as Fokker-Planck-Kolmogorov equation, stochastic averaging method, equivalent linearization, equivalent nonlinear system procedure and Monte Carlo simulation. The advantages and disadvantages of these methods are discussed, respectively. The state-of-the-art of the exact stationary solutions and approximately nonstationary solutions is also illustrated for the multi-degree-of-freedom nonlinear stochastic systems. Then, two effective procedures to evaluate the stochastic stability, i.e., the Lyapunov function and Lyapunov exponent, are briefly presented. Based on these two methods, the stochastic stability of multi-degree-of-freedom nonlinear stochastic systems is outlined. Finally, some suggestions are given for further research on the response and stability of nonlinear stochastic systems.

In this paper, the history of the Melnikov theory is summarized. In 1963, the classical Melnikov method was presented by Melnikov, a Russian scientist. Until now, the Melnikov theory has been extended and developed. The development of the Melnikov method is divided into three historical periods. The extension and application of Melnikov theory are respectively summed up in each historical period, in which the situation of study and main domestic and abroad results in this research field are enumerated. The relationships, problems and deficiencies are pointed out for a variety of Melnikov theories. In addition, another global perturbation method, i.e., energy phase theory, is set forth in order to compare with two theories which are normally used to investigate multi-pulse chaotic motion in the high-dimensional nonlinear systems. The brief history, the theory and the research achievements and engineering applications of the energy phase theory are elucidated. The origin of the energy phase theory and its inherent relations with the Melnikov theory are illustrated. The subject investigated in the energy phase method is contrast with that in the extended Melnikov method to find the difference between them. Disadvantages and open problems are indicated for both the energy phase method and the extended Melnikov method. Furthermore, theoretical frames of these two methods are stated briefly. The multi-pulse chaotic dynamics for a rectangular thin plate, simply supported at the fore-edge, is analyzed by using both of them. Numerical simulation further verifies the analytical prediction. Finally, deficiencies of these two theories are described in detail. The future development direction of the global perturbation theory is demonstrated too.

Friction has a significant effect, even dominant one in some cases, on the dynamic behavior of mechanical systems. Thorough investigation on friction dynamics is very important to avoid negative influences of friction on dynamical systems and make reasonable use of its beneficial effect. This paper outlines recent advances in the research of friction dynamics in mechanical systems. The friction model in common use, researches on the friction related self-excited, forced vibration and vibration control are presented. Besides the research methods, investigations on applications of friction dynamics are emphatically discussed, including the braking noise vibration, vibration energy dissipation and friction vibration control in a variety of fields.

The tethered satellite system, which is deployed from another ying vehicle in space via a tether, is a new technology for arti cial gravity creation, LEO to GEO tether transportation, scientific and technological applications, electro-dynamic study, and so on. This paper first surveys experimental researches of the tethered satellite systems on orbit, including the mission backgrounds, motivations, manipulate procedures and relevant experimental results. Then it reviews the con guration of ground-based experiments, covering both the equivalent principium and the experimental results. Finally, the paper addresses some open problems related to the tethered satellite technology to be developed in China.