Bifurcation study of transition to chaos in the oscillatory system of motion of a plate in a liquid

DOI10.20537/VM190101zbMath1448.34079OpenAlexW2947934944WikidataQ127759176 ScholiaQ127759176MaRDI QIDQ5114297

Tat'Yana Alekseevna Gurina

Publication date: 22 June 2020

Published in: Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/vuu661

zbMATH Keywords

chaoslimit cyclesingular pointattractorlargest Lyapunov exponenthomoclinic trajectorycascade of bifurcationsmotion of body in liquid

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Complex behavior and chaotic systems of ordinary differential equations (34C28) Attractors of solutions to ordinary differential equations (34D45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

• Plate falling in a fluid: regular and chaotic dynamics of finite-dimensional models
• On the problem of fall of a rigid body in a resisting medium
• Dynamical systems V. Bifurcation theory and catastrophe theory. Transl. from the Russian by N. D. Kazarinoff
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Visualization and analysis of invariant sets of dynamical systems.
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