Scenarios of Transitions to Hyperchaos in Nonideal Oscillating Systems
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We consider a class of nonideal oscillating (by Sommerfeld and Kononenko) dynamical systems and establish the existence of two types of hyperchaotic attractors in these systems. The scenarios of transitions from regular to chaotic ones attractors and the scenarios of transitions between chaotic attractors of different types are described.
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- 5.S. P. Kuznetsov, Dynamical Chaos [in Russian], Fizmatlit, Moscow (2006).Google Scholar
- 8.A. Yu. Shvets and V. A. Sirenko, “Specific features of transition to deterministic chaos in a nonideal hydrodynamic ‘tank filled with liquid – electric motor’ system,” Dinam. Sist.,1(29), No. 1, 113–131 (2011).Google Scholar
- 9.A. Yu. Shvets and V. A. Sirenko, “Unity and variety of the scenarios of transitions to chaos in the case of vibration of liquid in cylindrical tanks,” in: Proc. of the Institute of Mathematics, Ukrainian National Academy of Sciences “Mathematical Problems of Mechanics and Computational Mathematics,”11, No. 4 (2014), pp. 386–398.Google Scholar
- 10.A. Yu. Shvets and V. O. Sirenko, “New ways of transitions to deterministic chaos in nonideal oscillating systems,” Res. Bull. Nat. Tech. Univ. Ukraine “Kyiv Polytechnic Institute,”99, No. 1, 45–51 (2015).Google Scholar
- 11.V. O. Kononenko, Oscillating Systems with Bounded Excitations [in Russian], Nauka, Moscow (1964).Google Scholar
- 12.I. A. Lukovskii, Mathematical Models of Nonlinear Dynamics of Solid Bodies Filled with Liquids [in Russian], Naukova Dumka, Kiev (2010).Google Scholar
- 13.B. I. Rabinovich, Introduction to the Dynamics of Carrier Rockets of Spacecrafts [in Russian], Mashinostroenie, Moscow (1983).Google Scholar
- 14.R. A. Ibrahim, Liquid Sloshing Dynamics: Theory and Applications, Cambridge Univ. Press, Cambridge (2005).Google Scholar
- 15.A. Yu. Shvets, “Deterministic chaos of a spherical pendulum under bounded excitation” Ukr. Mat. Zh.,59, No. 4, 534–548 (2007); English translation:Ukr. Math. J.,59, No. 4, 602–614 (2007).Google Scholar
- 17.A. M. Samoilenko and N. I. Ronto, Numerical-Analytic Methods of Investigating Periodic Solutions, Mir, Moscow (1979).Google Scholar
- 18.T. S. Krasnopolskaya and A. Yu. Shvets, Regular and Chaotic Dynamics of Systems with Limited Excitation [in Russian], R&C Dynamics, Moscow (2008).Google Scholar
- 19.A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations. Invariant Tori [in Russian], Nauka, Moscow (1987).Google Scholar