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 nonautonomous predator-prey model with nonlinear diffusion and time delay. (English) Zbl 1147.34355
This paper deals with the uniform persistence and global stability of a nonautonomous predator-prey model with nonlinear diffusion and delay effect. The main technique is based on the construction of a suitable Lyapunov functional.

MSC:
34K20Stability theory of functional-differential equations
34K25Asymptotic theory of functional-differential equations
34K60Qualitative investigation and simulation of models
92D25Population dynamics (general)
WorldCat.org
Full Text: DOI
References:
[1] Levin, S. A.: Dispersion and population interaction. Am. nat. 108, 207-228 (1994)
[2] Allen, L. J. S.: Persistence and extinction in single-species reaction-diffusion models. Bull. math. Biol. 45, No. 2, 209-227 (1983) · Zbl 0543.92020
[3] Song, X. Y.; Chen, L. S.: Uniform persistence and global attractivity for nonautonomous competitive systems with dispersion. J. syst. Sci. complex. 15, 307-314 (2002) · Zbl 1027.92027
[4] Cui, J. A.; Chen, L. S.: Permanence and extinction in logistic and Lotka -- Volterra system with diffusion. J. math. Anal. appl. 258, No. 2, 512-535 (2001) · Zbl 0985.34061
[5] Beretta, E.; Takeuchi, Y.: Global asymptotic stability of Lotka -- Volterra diffusion models with continuous time delays. SIAM J. Appl. math. 48, 627-651 (1988) · Zbl 0661.92018
[6] Beretta, E.; Solimano, F.: Global stability and periodic orbits for two patch predator-prey diffusion delay models. Math. biosci. 85, 153-183 (1987) · Zbl 0634.92017
[7] Butler, G. J.; Freedman, H.; Waltman, P.: Uniformly persistent systems. Proc. am. Math. soc. 96, 425-429 (1986) · Zbl 0603.34043
[8] Freedman, H.; Waltman, P.: Persistence in models of three interacting predator-prey populations. Math. biosci. 68, 213-231 (1984) · Zbl 0534.92026
[9] Freedman, H.; Waltman, P.: Persistence in a model of three competitive populations. Math. biosci. 73, 89-101 (1985) · Zbl 0584.92018
[10] Song, X. Y.; Chen, L. S.: Optimal harvesting and stability with stage-structure for a two species competitive system. Math. biosci. 170, 173-186 (2001) · Zbl 1028.34049
[11] Gopalsamy, K.: Stability and oscillation in delay differential equations of population dynamics. (1992) · Zbl 0752.34039