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)
Bifurcations and chaos of the Bonhoeffer-van der Pol model. (English) Zbl 0677.92009
Summary: Periodic and chaotic behaviour of the Bonhoeffer-van der Pol model of a nerve membrane driven by a periodic stimulating current a 1 cosωt is investigated. Results show that there exist ordinary and reversed period-doubling cascades and a mode-locking state. At low driving amplitudes a 1 , there are period-doubling and chaotic states, but no impulse solutions. When a 1 is larger than a 0 =0·749, there are chaotic, reversed period-doubling, and mode-locking states and there also exist impulse trains. A mode-locking state with period 4 over a very large range of amplitudes is also found. At a 1 =1·7059 the system goes back to a one-period state.
MSC:
92CxxPhysiological, cellular and medical topics
34C05Location of integral curves, singular points, limit cycles (ODE)
34C25Periodic solutions of ODE