The disappearance of the limit cycle in a mode interaction problem with Z(2) symmetry

• Type: Article in International Scientific Journal
• Date: 1997

Authors

Sofia B. S. D. Castro (Author) FEP

Journal

Title: Nonlinearity

Vol. 10 No. 2

Pages: 425-432

ISSN: 0951-7715

Publisher: Institute of Physics Publishing

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-001-BXB

DOI: 10.1088/0951-7715/10/2/007

Abstract (EN): For a steady-state mode interaction problem with Z(2) symmetry Golubitsky, Stewart and Schaeffer (1988 Singularities and Groups in Bifurcation Theory vol II (New York: Springer) ch XIX) prove that there are parameter values for which a Hopf bifurcation occurs along a mixed-mode branch. The author has proved that it is always so in mode interaction problems with symmetry (Castro S B S D 1995 Mode interactions with symmetry Dyn. Stability Syst. 10 13-31). In this work, we are concerned with what happens to the limit cycle arising from this Hopf bifurcation. We find that, for certain parameter values, it vanishes through a homoclinic connection. To prove this, we-use Melnikov theory since the equations under study are a perturbation of Hamiltonian equations. This completes the bifurcation diagrams in Golubitsky et al (above).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 8