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)
Impulsive control of a Lotka-Volterra system. (English) Zbl 0949.93069
The following Lotka-Volterra population growth model $$\align \dot N_1 & =N_1(b_1+a_{11} N_1+a_{12} N_2+a_{13}N_3)\\ \dot N_2 & =N_2(b_2+a_{21} N_1+a_{22} N_2+a_{33} N_3)\\ \dot N_3 & =N_3(b_3+a_{31} N_1+ a_{32}N_2+ a_{33}N_3) \endalign$$ where $a_{ij}$ and $b_i$ $i,j=1,2,3$ are constants is considered. The dynamics of the processes is controlled via impulses of the $N_1$ process. At selected impulse instants, it is possible to switch the process to a new state. With this impulsive control the question is if it is possible to keep the processes $N_1$, $N_2$, $N_3$ from going extinct by stabilizing some positive point. Some stabilizability criteria are given and several examples are worked out.

93D15Stabilization of systems by feedback
92D25Population dynamics (general)
Full Text: DOI