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)
Ratio-dependent predator-prey system with stage structure for prey. (English) Zbl 1114.92056
Summary: A ratio-dependent predator-prey model with stage structure for the prey is proposed and analyzed, which improves the assumption that each individual prey has the same ability to be captured by a predator. In this paper, mathematical analysis of the model equations with regard to boundedness of solutions, nature of equilibria and permanence are analyzed. We obtain conditions that determine the permanence of the populations. Furthermore, we establish necessary and sufficient conditions for the local stability of the positive equilibrium of the model. By the application of comparing arguments and exploiting the monotonicity of one equation of the model, we obtain sufficient conditions for the global attractivity of the positive equilibrium.
MSC:
92D25Population dynamics (general)
34D05Asymptotic stability of ODE
34C60Qualitative investigation and simulation of models (ODE)
92D40Ecology