The Hopf-Hopf bifurcation with 2:1 resonance: periodic solutions and invariant tori

DOI10.3934/PROC.2015.1098zbMath1354.37054OpenAlexW2333476390MaRDI QIDQ260969

Dmitriy Yu. Volkov

Publication date: 22 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/proc.2015.1098

zbMATH Keywords

periodic solutioninvariant toriHopf-Hopf bifurcation

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Cites Work

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• The Andronov-Hopf bifurcation with \(2:1\) resonance
• 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
• A generic, hard transition to chaos
• Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation
• Chaos and the effect of noise in a model of three-wave mode coupling
• Classification and unfoldings of \(1:2\) resonant Hopf bifurcation
• Hopf bifurcation with non-semisimple 1:1 resonance
• The double Hopf bifurcation with 2:1 resonance
• Bifurcation and ’’strange’’ behavior in instability saturation by nonlinear three-wave mode coupling
• Unfoldings and bifurcations of quasi-periodic tori
• Elements of applied bifurcation theory

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