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)
Global analysis of Ivlev’s type predator-prey dynamic systems. (English) Zbl 1231.37054
Summary: Consider a class of Ivlev’s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.
37N25Dynamical systems in biology
92B05General biology and biomathematics
[1]Jitsuro Sugie. Two-parameter bifurcation in a predator-prey system of Ivelv type[J]. Journal of Mathematical Analysis and Application, 1998, 217(2):349–371. · Zbl 0894.34025 · doi:10.1006/jmaa.1997.5700
[2]Kooij R E, Zegeling A. A predator-prey model with Ivlev’s functional response[J]. Journal of Mathematical Analysis and Application, 1996, 198(2):473–489. · Zbl 0851.34030 · doi:10.1006/jmaa.1996.0093
[3]DeAngelis D L, Goldstein R A, O’Neill R V. A model for tropic interaction[J]. Ecology, 1975, 56:881–892. · doi:10.2307/1936298
[4]Tang Qiulin. A Predator-prey System with Ivlev’s Functional Response[J]. Journal of Beihua University(Natural Science), 2002, 3(5):381–384 (in Chinese).
[5]Feng Jianwen, Chen Shihua. Global asympotic behavior for the competing predators of the Ivlev types[J]. Mathematica Applicata, 2000, 13(4):85–88.