(NTU KhPI, 2016) Shvets, Aleksandr Yu.; Sirenko, Vasiliy
Some of non-ideal dynamic systems are considered. It is discovered and described the complicated transition
scenarios from regular to chaotic regimes and transitions between different types of chaotic regimes.
Described the transition to chaos, which begins by the Feigenbaum scenario, and ends by intermittency. Also
discusses the scenario of intermittency with several laminar phases and one turbulent phase. It is discovered
and described transitions "hyperchaotic attractor of one type – hyperchaotic attractor of another type," which
are realized according to the scenario of a generalized intermittency, but only with two rough-laminar phases.
The oscillating systems of a pendulum type, nonideal in the sense of Sommerfeld-Kononenko are considered. Such systems are used for modeling oscillations in hydrodynamics, shell theory and other applications. The complex scenario of transition to the hyperchaos is revealed and described in details. Revealed scenario
begins with symmetric limit cycles and ends with a transition to hyperchaos through generalized intermittency with two coarse grained laminar phases. This scenario is illustrated in detail by projections of phase portraits, Poincaré sections and other characteristics of attractors of the system.