zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Hopf bifurcation in differential equations with delay for tumor-immune system competition model. (English) Zbl 1156.34066
A model that refers to the competition between the immune system and an aggressive host such as a tumor is introduced. The model which describes this competition is governed by a system of differential equations with one delay. It is shown that the dynamics depends crucially on the time delay parameter. By using the time delay as bifurcation parameter, the analysis is focused on the Hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the nontrivial steady state. The obtained results depict the oscillations, given by simulations [see {\it M. Galach}, Int. J. Appl. Math. Comput. Sci. 13, 395--406 (2003; Zbl 1035.92019)], which are observed in reality [see {\it D. Kirschner} and {\it J. C. Panetta}, J. Math. Biol. 37, 235--252 (1998; Zbl 0902.92012)].

34K60Qualitative investigation and simulation of models
34K18Bifurcation theory of functional differential equations
34K13Periodic solutions of functional differential equations
92C37Cell biology
Full Text: DOI