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)
Asymptotic behaviour of the stochastic Gilpin-Ayala competition models. (English) Zbl 1195.34083
Summary: We investigate a stochastic Gilpin-Ayala competition system, which is more general and more realistic than the classical Lotka-Volterra competition system. We discuss the asymptotic behaviour in detail of the stochastic Gilpin-Ayala competition system, and compare the classical Lotka-Volterra with Gilpin-Ayala competition system.
MSC:
34F05ODE with randomness
92D25Population dynamics (general)
34D05Asymptotic stability of ODE
References:
[1]Arató, M.: A famous nonlinear stochastic equation (Lotka – Volterra model with diffusion), Math. comput. Modelling 38, 709-726 (2003) · Zbl 1049.92030 · doi:10.1016/S0895-7177(03)90056-2
[2]Mao, X.; Marion, G.; Renshaw, E.: Environmental Brownian noise suppresses explosions in populations dynamics, Stochastic process. Appl. 97, 95-110 (2002) · Zbl 1058.60046 · doi:10.1016/S0304-4149(01)00126-0
[3]Mao, X.; Sabanis, S.; Renshaw, E.: Asymptotic behaviour of the stochastic Lotka – Volterra model, J. math. Anal. appl. 287, 141-156 (2003) · Zbl 1048.92027 · doi:10.1016/S0022-247X(03)00539-0
[4]Takeuchi, Y.: Diffusion effect on stability of Lotka – Volterra models, Bull. math. Biol. 48, 585-601 (1986) · Zbl 0613.92025
[5]Fan, M.; Wang, K.: Global periodic solutions of a generalized n-species gilpin – ayala competition model, Comput. math. Appl. 40, 1141-1151 (2000) · Zbl 0954.92027 · doi:10.1016/S0898-1221(00)00228-5
[6]Gilpin, M. E.; Ayala, F. J.: Global models of growth and competition, Proc. natl. Acad. sci. USA 70, 3590-3593 (1973) · Zbl 0272.92016 · doi:10.1073/pnas.70.12.3590
[7]Lian, B.; Hu, S.: Stochastic delay gilpin – ayala competition models, Stoch. dyn. 6, No. 4, 561-576 (2006) · Zbl 1117.34079 · doi:10.1142/S0219493706001888