Extending slow manifolds near transcritical and pitchfork singularities

Authors
Krupa, M Szmolyan, P
Citation
M. Krupa et P. Szmolyan, Extending slow manifolds near transcritical and pitchfork singularities, NONLINEARIT, 14(6), 2001, pp. 1473-1491
Citations number
16
Categorie Soggetti
Mathematics
Journal title
NONLINEARITY
ISSN journal
09517715 → ACNP
Volume
14
Issue
6
Year of publication
2001
Pages
1473 - 1491
Database
ISI
SICI code
0951-7715(200111)14:6<1473:ESMNTA>2.0.ZU;2-6
Abstract
We consider the dynamics of singularly perturbed differential equations nea r points where the critical manifold has a transcritical or a pitchfork sin gularity. Our main tool is the recently developed blow-up method, which all ows a detailed geometric analysis of such problems. A version of the Melnik ov method to study transversality properties in this and related problems i s developed.