Typical and generalized transitions to deterministic chaos for atypical attractors of non-ideal dynamic systems





non-ideal dynamic system, regular maximal attractor, chaotic maximal attractor, typical and generalized intermittency


Some applied nonlinear, non-ideal dynamic systems of the fifth order, which are used to describe the oscillations of spherical pendulums and in hydrodynamics, are considered. Maximal attractors, both regular and chaotic, of such systems are constructed. Various bifurcations of maximal attractors are discussed. The transition to deterministic chaos is established for maximal attractors in typical Feigenbaum and Manneville–Pomeau scenarios. The implementation of the generalized alternation scenario for chaotic maximum attractors of such systems is investigated. A sign of the implementation of the scenario of generalized alternation has been revealed.

Author Biography

Aleksandr Shvets, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Doctor of Physical and Mathematical Sciences, a professor at the Department of Mathematical Physics and Differential Equations of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.


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Mathematical methods, models, problems and technologies for complex systems research