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)
Dynamic of a stochastic predator-prey population. (English) Zbl 1238.92055
Summary: A stochastic predator-prey model is studied. First we prove the existence, uniqueness and positivity of solutions. Then we show the upper bounds for the moments and the growth rate of the population. In some cases, the growth rate is negative and the population dies out rapidly. The paper ends with some reviews of the paper of {\it B.G. Zhang} and {\it K. Gopalsamy}, Stochastic Anal. Appl. 18, No. 2, 323--331 (2000; Zbl 0983.92023).

60H10Stochastic ordinary differential equations
34F05ODE with randomness
Full Text: DOI
[1] Arnold, L.: Stochastic differential equations: theory and applications, (1972) · Zbl 0216.45001
[2] Beddington, J. R.: Mutual interference between parasites or predators and its effect on searching efficiency, J. animal ecol. 44, No. 1, 331-340 (1975)
[3] Cantrell, R. S.; Cosner, C.: On the dynamics of predator -- prey models with the bedding -- deangelis functional response, J. math. Anal. appl. 257, 206-222 (2001) · Zbl 0991.34046 · doi:10.1006/jmaa.2000.7343
[4] Deangelis, D. L.; Goldstein, R. A.; O’neill, R. V.: A model for trophic interaction, Ecology 56, 881-892 (1975)
[5] Fan, M.; Kuang, Y.: Dynamics of a non-autonomous predator -- prey system with the beddington -- deangelis functional response, J. math. Anal. appl. 295, 15-39 (2004) · Zbl 1051.34033 · doi:10.1016/j.jmaa.2004.02.038
[6] Friedman, A.: Stochastic differential equations and their applications, (1976) · Zbl 0323.60057
[7] Hwang, T.: Global analysis of the predator -- prey system with beddington -- deangelis functional response, J. math. Anal. appl. 281, 395-401 (2003) · Zbl 1033.34052 · doi:10.1016/S0022-247X(02)00395-5
[8] Ioannis, K.; Steven, E. S.: Brownian motion and stochastic calculus, (1991) · Zbl 0734.60060
[9] X. Mao, Stochastic Differential Equations and Applications, Horwood, 1997. · Zbl 0892.60057
[10] Mao, X.; Deng, F.; Luo, Q.; Pang, S.: Noise suppresses or expresses exponential growth, Syst. control lett. 57, 262-270 (2008) · Zbl 1157.93515 · doi:10.1016/j.sysconle.2007.09.002
[11] Mao, X.; Hu, G.; Liu, M.; Song, M.: Noise suppresses exponential growth under regime switching, J. math. Anal. appl. 355, 783-795 (2009) · Zbl 1173.60024 · doi:10.1016/j.jmaa.2009.02.009
[12] Mao, X.; Marion, G.; Renshaw, E.: Environmental Brownian noise suppresses explosions in population dynamics, Stoch. proc. Appl. 97, 95-110 (2002) · Zbl 1058.60046 · doi:10.1016/S0304-4149(01)00126-0
[13] Zhang, B. G.; Gopalsamy, K.: On the periodic solution of N-dimentional stochastic population models, Stoch. anal. Appl. 18, No. 2, 323-331 (2000) · Zbl 0983.92023 · doi:10.1080/07362990008809671