Author:
Moza Gheorghe, ,Sterpu Mihaela,Rocşoreanu Carmen, ,
Abstract
<abstract><p>The generic double-Hopf bifurcation is presented in detail in literature in textbooks like references. In this paper we complete the study of the double-Hopf bifurcation with two degenerate (or nongeneric) cases. In each case one of the generic conditions is not satisfied. The normal form and the corresponding bifurcation diagrams in each case are obtained. New possibilities of behavior which do not appear in the generic case were found.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference18 articles.
1. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Third Edition, Springer–Verlag, New York, 2004. https://doi.org/10.1007/978-1-4757-3978-7
2. S. N. Chow, C. Li, D. Wang, Normal Forms and Bifurcation of Planar Vector Fields, Cambridge University Press, Cambridge and New York, 1994. https://doi.org/10.1017/CBO9780511665639
3. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer, 1983. https://doi.org/10.1007/978-1-4612-1140-2
4. G. Revel, D. M. Alonso, J. L. Moiola, A degenerate 2:3 resonant Hopf–Hopf bifurcation as organizing center of the dynamics: numerical semiglobal results, SIAM J. Appl. Dyn. Syst., 14 (2015), 1130–1164. https://doi.org/10.1137/140968197
5. N. K. Gavrilov, Bifurcations of an equilibrium with one zero and a pair of pure imaginary roots, Methods Qual. Theory Differ. Equations, 1987.
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