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)
Global stability in a population model with piecewise constant arguments. (English) Zbl 1177.34097

Summary: We investigate the global stability and the boundedness character of the positive solutions of the differential equation

dx dt=r-x(t){1-α·x(t)-β 0 x([t])-β 1 x([t-1])}

where t>0, the parameters r, α, β 0 and β 1 denote positive numbers and [t] denotes the integer part of t[0,). We consider the discrete solution of the logistic differential equation to show the global asymptotic behavior and obtained that the unique positive equilibrium point of the differential equation is a global attractor with a basin that depends on the conditions of the coefficients. Furthermore, we studied the semi-cycle of the positive solutions of the logistic differential equation.

34K20Stability theory of functional-differential equations
34K12Growth, boundedness, comparison of solutions of functional-differential equations
39A12Discrete version of topics in analysis