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)
Permanence for a delayed discrete ratio-dependent predator-prey model with monotonic functional responses. (English) Zbl 1167.34359
Summary: A delayed discrete ratio-dependent predator-prey model with monotonic functional responses is proposed. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system.

MSC:
34D05Asymptotic stability of ODE
34K05General theory of functional-differential equations
92D25Population dynamics (general)
92D40Ecology
WorldCat.org
Full Text: DOI
References:
[1] Fan, Y. H.; Li, W. T.: Permanence in delayed ratio-dependent predator--prey models with monotonic functional responses. Nonlinear anal. 8, 424-434 (2007) · Zbl 1152.34368
[2] Xu, C. Y.; Wang, M. J.: Permanence for a delayed discrete three-level food-chain model with beddington-deangelis functional response. Appl. math. Comput. 187, 1109-1119 (2007) · Zbl 1120.92049
[3] Agarwal, R. P.: Difference equations and inequalities: theory, method and applications, monographs and textbooks in pure and applied mathematics. 228 (2000)
[4] Agarwal, R. P.; Wong, P. J. Y.: Advance topics in difference equations. (1997) · Zbl 0878.39001
[5] Freedman, H. I.: Deterministic mathematics models in population ecology. (1980) · Zbl 0448.92023
[6] Murry, J. D.: Mathematical biology. (1989)
[7] Gopalsamy, K.: Stability and oscillations in delay differential equations of population dynamics. (1992) · Zbl 0752.34039
[8] Takeuchi, Y.: Global dynamical properties of Lotka--Volterra systems. (1996) · Zbl 0844.34006
[9] Wang, L.; Wang, M. Q.: Ordinary difference equation. (1991) · Zbl 0734.34024
[10] Chen, F. D.: Permanence and global attractivity of a discrete multispecies Lotka-Volterra competition predator--prey systems. Appl. math. Comput. 182, 3-12 (2006) · Zbl 1113.92061