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)
A brief survey of persistence in dynamical systems. (English) Zbl 0756.34054
Delay differential equations and dynamical systems, Proc. Conf., Claremont/CA (USA) 1990, Lect. Notes Math. 1475, 31-40 (1991).
[For the entire collection see Zbl 0727.00007.] The differential system $x\sb i'=x\sb if\sb i(x\sb 1\dots x\sb n)$ $(i=1,\dots,n)$ is said to be persistent if $\liminf\sb{t\to+\infty}x\sb i(t)\to 0$ when $x\sb i(0)>0$ $(i=1,\dots,n)$. These systems describe the dynamics of interacting populations in a closed environment and the persistence implies the survival of all the components of the ecosystem. The author gives a description of the mathematical models connected with these biological situations distinguishing two approaches: the analysis of the flow on the boundary and the use of a Lyapunov-like function. In the survey there are no proofs of the theorems but many examples and updated references.

34D05Asymptotic stability of ODE
34C11Qualitative theory of solutions of ODE: growth, boundedness
92D25Population dynamics (general)
34-02Research monographs (ordinary differential equations)