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)
Uniqueness of limit cycles in Gause-type models of predator-prey systems. (English) Zbl 0642.92016
Summary: This paper deals with the question of uniqueness of limit cycles in predator-prey systems of Gause type. By utilizing several transformations, these systems are reduced to a generalized Lienard system as discussed by L. A. Cherkas and L. I. Zhilevich [Differ. Uravn. 6, 1170-1178 (1970; Zbl 0213.364)] and by Z. Zhang [Appl. Anal. 23, 63-76 (1986; Zbl 0582.34038)]. As a consequence, criteria for the uniqueness of limit cycles are derived, which include results of K.-S. Cheng [SIAM J. Math. Anal. 12, 541-548 (1981; Zbl 0471.92021)] and are related to results of L.-P. Liou and K.-S. Cheng (to appear). Several examples are given to illustrate our results.

MSC:
92D25Population dynamics (general)
34C05Location of integral curves, singular points, limit cycles (ODE)