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)
Formation and propagation of localized states in extended systems. (English) Zbl 1108.35386
Summary: We study a one-species-diffusion equation supplemented by a nonlinear saturation term. If this term includes temporal delay, a rich spatio-temporal behavior already at the critical point where the steady homogeneous solution gets unstable is expected. Normal form transformation into a complex Ginzburg-Landau equation shows that the condition for phase turbulence is always fulfilled. As a secondary instability of these chaotic states well ordered spiral waves and targets are found numerically. Here the system shows features well-known from excitable media. Finally we propose the construction of logical circuits by means of a network built up by one-dimensional excitable media.
MSC:
35Q80Appl. of PDE in areas other than physics (MSC2000)
92C15Developmental biology, pattern formation