Donetskyi S. New types of attractors in nonideal dynamic systems

The thesis is devoted to the study of limit sets of two nonideal according to Sommerfeld-Kononenko dynamic systems: the «LC-generator – piezoceramic transducer» system and the «spherical pendulum – electric motor» system. The main results that determine the scientific novelty of the thesis are as follows.For the «generator -- piezoceramic transducer» system: 1. An atypical alternation of the Feigenbaum and Manneville-Pomeau scenarios during transitions from regular to chaotic regimes has been revealed. 2. The values of the parameters for which two attractors coexist in the system, with one attractor located in the area of localization of the other, have been found. 3. The coexistence of the following attractors has been established: quasi-periodic and periodic; periodic and periodic; chaotic and periodic. 4. The coexisting attractors of this system have been identified in accordance to «rare» and «hidden» classification. 5. The effect of delay on the classification of coexisting attractors in terms of «rare» and «hidden» has been analyzed. For the «spherical pendulum -- electric motor» system: 1. Isolated and non-isolated equilibrium positions have been revealed. 2. Regular and chaotic families of non-isolated limit sets with attractive properties have been discovered. 3. It has been shown that families of non-isolated limit sets with attractive properties are not attractors in the «classical» sense but correspond to the definition of a maximal attractor. 4. The scenarios of transition to chaos of maximal attractors have been found to follow similar patterns as the scenarios of transition to chaos observed for «classical» attractors. 5. The theorems regarding the stability of an isolated equilibrium position and the existence of a family of non-isolated equilibrium positions have been proven.