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)
Rich dynamics of a ratio-dependent one-prey two-predators model. (English) Zbl 1007.34054
A ratio-dependent predator-prey model is the one where the interaction term has the form xy/(ax+y) where x is the prey density, y is the predator density and a is a constant. The validity of such models is still debatable. Here, a one-prey two-predators model is studied. The authors argue that the ratio dependent model give two important realistic results: The first is the existence of a stable low density prey equilibrium. The second is a simultaneous extinction. The authors derive sufficient conditions for the competitive exclusion (one predator goes extinct). They also derive conditions for a predator to be a system saver, i.e. a predator whose introduction prevents the prey from going extinct. Moreover, conditions for total extinction and for coexistence are derived.
Reviewer: E.Ahmed (Al-Ain)
MSC:
34D30Structural stability of ODE and analogous concepts
92D25Population dynamics (general)
34D05Asymptotic stability of ODE
34D20Stability of ODE