Asymptotic Unfoldings of Dynamical Systems by Normalizing beyond the Normal Form

Journal of Differential Equations

Volumn 143, Issue 1, 1998, Pages 151-190

  Murdock, James ^a  

^a IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008836560     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1997.3368     Document Type: Article

References (7)

1. Chow Shui-Nee, Li Chengzhi, Wang Duo. Normal Forms and Bifurcation of Planar Vector Fields. 1994;Cambridge Univ. Press, Cambridge.
2. Elphick C., Tirapegui E., Brachet M. E., Coullet P., Iooss G. A simple global characterization for normal forms of singular vector fields. Physica D. 29:1987;95-127.
3. Guckenheimer John, Holmes Philip. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. 1983;Springer-Verlag, New York.
4. Huseyin K. Bifurcations associated with a three-fold zero eigenvalue. Quart. Appl. Math. 46:1988;193-216.
5. Murdock J. Qualitative theory of nonlinear reasonance by averaging and dynamical systems methods. Dynamics Reported. 1:1988;91-172.
6. van Gils S. A., Krupa M., Langford W. F. Hopf bifurcation with non-semisimple 1:1 resonance. Nonlinearity. 3:1990;825-850.
7. Wiggins S. Introduction to Applied Nonlinear Dynamical Systems and Chaos. 1990;Springer-Verlag, New York.