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)
Dynamic behaviors of a harvesting Leslie-Gower predator-prey model. (English) Zbl 1213.37129
Summary: A Leslie-Gower predator-prey model incorporating harvesting is studied. By constructing a suitable Lyapunov function, we show that the unique positive equilibrium of the system is globally stable, which means that suitable harvesting has no influence on the persistent property of the harvesting system. After that, detailed analysis about the influence of harvesting is carried out, and an interesting finding is that under some suitable restriction, harvesting has no influence on the final density of the prey species, while the density of predator species is strictly decreasing function of the harvesting efforts. For the practical significance, the economic profit is considered, sufficient conditions for the presence of bionomic equilibrium are given, and the optimal harvesting policy is obtained by using the Pontryagin’s maximal principle. At last, an example is given to show that the optimal harvesting policy is realizable.
37N25Dynamical systems in biology
92D25Population dynamics (general)