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)
Almost-periodic solutions of a delay population equation with feedback control. (English) Zbl 1128.34045
Consider the delay differential system $$\align\frac{dx}{dt}(t) & = x(t)[r(t)-a(t)x(t)-x(t-\tau)-c(t)u(t)],\\ \frac{du}{dt}(t) & =-\eta(t)u(t)+g (t)x(t-\tau), \tag *\endalign$$ where $\tau>0$, the functions $r,a,c,\eta$ and $g$ are almost-periodic. The authors derive conditions ensureing a unique almost periodic solution with the properties: (i) All components are positive for all time. (ii) It is uniformly asymptotically stable. (iii) The frequency module is contained in the frequency module of $r,a,c,\eta$ and $g$.

34K14Almost and pseudo-periodic solutions of functional differential equations
92D25Population dynamics (general)
34K35Functional-differential equations connected with control problems
Full Text: DOI
[1] Chen, F. D.: Positive periodic solutions of neutral Lotka -- Volterra system with feedback control. Appl. math. Comput. 162, No. 3, 1279-1302 (2005) · Zbl 1125.93031
[2] Chen, F. D.; Lin, S. J.: Periodicity in a logistic type system with several delays. Comput. math. Appl. 48, No. 1 -- 2, 35-44 (2004) · Zbl 1061.34050
[3] Chen, F. D.; Lin, F. X.; Chen, X. X.: Sufficient conditions for the existence of positive periodic solutions of a class of neutral delay models with feedback control. Appl. math. Comput. 158, No. 1, 45-68 (2004) · Zbl 1096.93017
[4] Chen, F. D.; Sun, D. X.; Lin, F. X.: Periodicity in a food-limited population model with toxicants and state dependent delays. J. math. Anal. appl. 288, No. 1, 132-142 (2003)
[5] Fink, A. M.: Almost periodic differential equations. Lecture notes on mathematics 377 (1974) · Zbl 0325.34039
[6] Gopalsamy, K.: Stability and oscillation in delay differential equations of population dynamics. Mathematic and its applications 74 (1992) · Zbl 0752.34039
[7] Gopalsamy, K.; Weng, P. X.: Feedback regulation of logistic growth. Internat. J. Math. sci. 16, No. 1, 177-192 (1993) · Zbl 0765.34058
[8] He, C. Y.: Almost periodic differential equations. (1992)
[9] Seifert, G.: On a delay-differential equation for single specie population variation. Nonlinear anal. TMA 11, 1051-1059 (1987) · Zbl 0629.92019
[10] Weng, P. X.: Global attractivity in a periodic competition system with feedback controls. Acta appl. Math. 12, 11-21 (1996) · Zbl 0859.34061
[11] Weng, P. X.: Existence and global stability of positive periodic solution of periodic integro-differential systems with feedback controls. Comput. math. Appl. 40, 747-759 (2000) · Zbl 0962.45003
[12] Xiao, Y. N.; Tang, S. Y.; Chen, J. F.: Permanence and periodic solution in a competition system with feedback controls. Math. comput. Modelling 27, No. 6, 33-37 (1998) · Zbl 0896.92032
[13] Yang, F.; Jiang, D. Q.: Existence and global attractivity of positive periodic solution of a logistic growth system with feedback control and deviating arguments. Ann. differential equations 17, No. 4, 337-384 (2001) · Zbl 1004.34030
[14] Yoshizawa, T.: Stability theory and the existence of periodic solutions and almost periodic solutions. Applied mathematical sciences 14 (1975) · Zbl 0304.34051
[15] Yuan, R.: The existence of almost periodic solution of a population equation with delay. Appl. anal. 61, 45-52 (1999)