zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Bifurcation of a limit cycle in the ac-driven complex Ginzburg-Landau equation. (English) Zbl 1197.35039
Summary: Stability and dynamic bifurcation in the ac-driven complex Ginzburg-Landau equation with periodic boundary conditions and even constraint are investigated using central manifold reduction procedure and attractor bifurcation theory. The results show that the bifurcation into an attractor near a small-amplitude limit cycle takes place on a two dimensional central manifold, as bifurcation parameter crosses a critical value. Furthermore, the component of the bifurcated attractor is analytically described for the non-autonomous system.
MSC:
35B32Bifurcation (PDE)
35K20Second order parabolic equations, initial boundary value problems
37G10Bifurcations of singular points
35K58Semilinear parabolic equations
35B35Stability of solutions of PDE