A "flexible-rotor/limited-power-excitation-source" dynamical system, which is a model of the vibrations of shafts driven by a motor of limited power is considered. The types of rotation characteristics of the motor and resonance characteristics of the shaft in the resonance parameter zone for different values of the viscosity coefficient of the medium are investigated. These characteristics completely describe the dynamics of the system when its parameters vary.@en

The existence and stability of stationary cluster structures in uniform chains of dissipatively coupled rotators is investigated. Cluster synchronization is interpreted as the classical synchronization of cluster rotators, which are elementary structure-forming objects. The complete set of types of cluster rotators and simple cells is defined. This definition is equivalent to the definition of the complete set of types of cluster structures. The completeness of this set is proved. The problem of the stability of cluster structures is solved. Physical examples of chains of rotators and a physical interpretation of the results of this research are given.@en

Asymptotic theory of synchronization of chaotic oscillations of non-identical dynamic systems with dissipative connection is proposed. Various cases of the non-identity degree, when the synchronization is asymptotically close to the identical one, are considered for the dynamic systems and their connections. The theory covers both mutual and forced synchronization of systems including systems having slowly changing parameters. The general definition of synchronization and the integral variety method are assumed as a basis of the theory. Results of numerical experiment are given.@en

The dynamics of a vibrational mechanism with an energy source of limited power is considered. A system of two degrees of freedom is reduced to a system of the Lorenz type by the method of averaging. The existence of one of the types of chaotic attractors in a dynamical system which is a vibrational mechanism, that is, a Lorenz attractor, is established by this. The existence of a Feigenbaum attractor and intermittence is also established. Chaotic limit sets determine the chaotic behaviour of the instantaneous frequency of rotation of an asynchronous motor. The qualitative patterns of the rotational characteristic are constructed for different values of the parameters of the system and a physical interpretation of the results is given.@en