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)
Dynamics of a class of nonautonomous semi-ratio-dependent predator–prey systems with functional responses. (English) Zbl 1029.34042

The authors give an in-depth study of various properties of solutions to the system

x ' =x[a(t)-b(t)x]-c(t,x)y,y ' =y[d(t)-e(t)y/x],

which contains a number of special cases arising in applications. State of the art is shown by an extensive bibliography. Under several hypotheses on the coefficients of the system, the ultimate boundedness of solutions and the permanence of the system (as defined in the paper) are proved.

By adding the assumption of periodicity (almost-periodicity) of the coefficients, the existence and the uniqueness of positive periodic (almost-periodic) solutions are proved. In addition, the considered solutions are globally asymptotically stable (as defined in the paper) in all the three cases.

34D40Ultimate boundedness (MSC2000)
34D05Asymptotic stability of ODE