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)
Stable periodic solution of the discrete periodic Leslie-Gower predator-prey model. (English) Zbl 1067.39008
For the system ${x}_{1}\left(k+1\right)={x}_{1}\left(k\right)exp\left\{{r}_{1}-{b}_{1}{x}_{1}\left(k\right)-{a}_{1}{x}_{2}\left(k\right)\right\}$, ${x}_{2}\left(k+1\right)={x}_{2}\left(k\right)exp\left\{{r}_{2}-{a}_{2}{x}_{2}\left(k\right)/{x}_{1}\left(k\right)\right\}$ a sufficient condition is given such that it is permanent. In the case of periodic coefficients sufficient conditions are given such that a periodic solution exists, and that this solution is globally stable, in case it is positive.
MSC:
 39A11 Stability of difference equations (MSC2000) 92D25 Population dynamics (general)