Bifurcation formulae derived from center manifold theory

DOI10.1016/0022-247X(78)90120-8zbMath0435.34034OpenAlexW2023941568MaRDI QIDQ1140206

Yieh-Hei Wan, Brian Hassard

Publication date: 1978

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

Full work available at URL: https://doi.org/10.1016/0022-247x(78)90120-8

zbMATH Keywords

center manifold theoremN-dimensional Hopf bifurcation theoryPoincare normal formreal canonical form

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
• 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

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