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)
Diffusion-mediated persistence in two-species competition Lotka-Volterra model. (English) Zbl 0671.92022
Summary: We consider a system composed of two Lotka-Volterra patches connected by diffusion. Each patch has two competitors. Conditions for persistence of the system are given. It is proved that the system can be made persistent under appropriate diffusion coefficients ensuring the instability of boundary equilibria, even if each species is not persistent within each patch. The choice of the coefficients depends closely on the patch dynamics without diffusion.

MSC:
92D25Population dynamics (general)
34C99Qualitative theory of solutions of ODE
92D40Ecology
37N99Applications of dynamical systems
37-99Dynamic systems and ergodic theory (MSC2000)
WorldCat.org
Full Text: DOI
References:
[1] Freedman, H. I.: Deterministic mathematical models in population ecology. (1980) · Zbl 0448.92023
[2] H.I. Freedman and Y. Takeuchi, Global stability and predator dynamics in a model of prey dispersal in a patchy environment, Nonlinear Analy., to appear. · Zbl 0685.92018
[3] H.I. Freedman and Y. Takeuchi, Predator survival versus extinction as a function of dispersal in a predator-prey model with patchy environment, Appl. Analy., to appear. · Zbl 0641.92016
[4] Freedman, H. I.; Waltman, P.: Mathematical models of population interaction with dispersal. I. stability of two habitats with and without a predator. SIAM J. Appl. math. 32, 631-648 (1977) · Zbl 0362.92006
[5] Freedman, H. I.; Waltman, P.: Persistence in models of three interacting predator--prey populations. Math. biosci. 68, 213-231 (1984) · Zbl 0534.92026
[6] Freedman, H. I.; Waltman, P.: Persistence in a model of three competitive populations. Math. biosci. 73, 89-101 (1985) · Zbl 0584.92018
[7] Hutson, V.: Predator mediated coexistence with a switching predator. Math. biosci. 68, 233-246 (1984) · Zbl 0534.92027
[8] Hutson, V.; Vickers, G. T.: A criterion for permanent coexistence of species, with an application to a two-prey, one-prediator system. Math. biosci. 63, 253-269 (1983) · Zbl 0524.92023
[9] Kirlinger, G.: Permanence in Lotka-Volterra equations: linked prey-predator systems. Math. biosci. 82, 165-191 (1986) · Zbl 0607.92022
[10] Levin, S. A.: Spatial patterning and the structure of ecological communities. Some mathematical questions in biology, 1-35 (1976)
[11] Seneta, E.: Non-negative matrices. (1973) · Zbl 0278.15011
[12] J.W.-H.^So, Persistence and extinction in a predator-prey model consisting of nine prey genotypes (preprint). · Zbl 0708.92011
[13] Takeuchi, Y.; Adachi, N.: Existence and bifurcation of stable equilibrium in two-prey, one-predator communities. Bull. math. Biol. 45, 877-900 (1983) · Zbl 0524.92025