Ljapunov approach to multiple Hopf bifurcation

DOI10.1016/0022-247X(79)90195-1zbMath0444.34040MaRDI QIDQ1144715

F. Göbber, K.-D. Williamowski

Publication date: 1979

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

algorithmlimit cyclesfocal valuesLjapunov's direct methodmultiple bifurcationmultiple Hopf bifurcationsystem of two variables

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Dynamical systems and ergodic theory (37-XX)

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Cites Work

• Bifurcation formulae derived from center manifold theory
• Bifurcation phenomena in FitzHugh's nerve conduction equations
• An applicable Hopf bifurcation formula and instability of small periodic solutions of the Field-Noyes model
• 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
• Generation of the nervous impulse and periodic oscillations
• On the theory and application of the Hopf-Friedrich Bifurcation theory
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