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)
Stability and bifurcation analysis in van der Pol’s oscillator with delayed feedback. (English) Zbl 1237.70091
Summary: The classical van der Pol equation with delayed feedback and a modified equation where a delayed term provides the damping are considered. Linear stability of the equations is investigated by analyzing the associated characteristic equations. It is found that there exist the stability switches when delay varies, and the Hopf bifurcation occurs when the delay passes through a sequence of critical values. The bifurcation diagram is drawn in (ϵ,k)-plane, and the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem.
MSC:
70K50Transition to stochasticity (general mechanics)
34K20Stability theory of functional-differential equations
34K18Bifurcation theory of functional differential equations