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

• Tipo: Artigo em Revista Científica Internacional
• Data: 1997

Autores

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

Revista

Título: Nonlinearity

Vol. 10 Nº 2

Páginas: 425-432

ISSN: 0951-7715

Editora: Institute of Physics Publishing

Indexação

ISI Web of Knowledge - 1 Citação

Scopus - 1 Citação

Outras Informações

ID Authenticus: 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).

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 8