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)
Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay. (English) Zbl 1104.92065
Summary: A two-dimensional delayed continuous-time dynamical system modeling a predator-prey food chain, and based on a modified version of Holling type-II scheme, is investigated. By constructing a Lyapunov function, we obtain a sufficient condition for global stability of the positive equilibrium. We also present some related qualitative results for this system.

MSC:
92D40Ecology
34D20Stability of ODE
34D23Global stability of ODE
65L99Numerical methods for ODE
WorldCat.org
Full Text: DOI
References:
[1] Aziz-Alaoui, M. A.: Study of Leslie -- gower-type tritrophic population. Chaos solitons fractals 14, No. 8, 1275-1293 (2002) · Zbl 1031.92027
[2] Aziz-Alaoui, M. A.; Okiye, M. Daher: Boundeness and global stability for a predator -- prey model with modified Leslie -- gower and Holling-typeii schemes. Appl. math. Lett. 16, 1069-1075 (2003) · Zbl 1063.34044
[3] Beretta, E.; Kuang, Y.: Global analyses in some delayed ratio-depended predator -- prey systems. Nonlinear anal. Theory methods appl. 32, No. 3, 381-408 (1998) · Zbl 0946.34061
[4] Kuang, Y.: Delay differential equations, with applications in population dynamics. (1993) · Zbl 0777.34002
[5] Upadhyay, R. K.; Rai, V.: Crisis-limited chaotic dynamics in ecological systems. Chaos solitons fractals 12, No. 2, 205-218 (2001) · Zbl 0977.92033
[6] Upadhyay, R. K.; Iyengar, S. R. K.: Effect of seasonality on the dynamics of 2 and 3 species prey -- predator system. Nonlinear anal.: real world appl. 6, 509-530 (2005) · Zbl 1072.92058
[7] Xu, R.; Chaplain, M. A. J.: Persistence and global stability in a delayed predator -- prey system with michaelis -- menten type functional response. Appl. math. Comput. 130, 441-455 (2002) · Zbl 1030.34069