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 discrete almost periodic logistic equation. (English) Zbl 1185.39011
Summary: We consider an almost periodic discrete logistic equation. Sufficient conditions are obtained for the existence of a unique almost periodic solution which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result.

39A24Almost periodic solutions (difference equations)
Full Text: DOI
[1] Coleman, B. D.: Nonautonomous logistic equations as models of the adjustment of populations to environmental changes, Math. biosci. 45, 159-173 (1979) · Zbl 0425.92013 · doi:10.1016/0025-5564(79)90057-9
[2] Coleman, B. D.; Hsieh, Y. H.; Knowles, G. P.: On the optimal choice of r for a population in a periodic environment, Math. biosci. 46, 71-85 (1979) · Zbl 0429.92022 · doi:10.1016/0025-5564(79)90015-4
[3] Gopalsamy, K.; He, X. Z.: Dynamics of an almost periodic logistic integrodifferential equation, Methods appl. Anal. 2, 38-66 (1995) · Zbl 0835.45004
[4] Hallam, T. G.; Clark, C. E.: Nonautonomous logistic equations as models of populations in a deteriorating environment, J. theoret. Biol. 93, 301-311 (1981)
[5] Gopalsamy, K.: Stability and oscillations in delay differential equations of population dynamics, mathematics and its applications, Stability and oscillations in delay differential equations of population dynamics, mathematics and its applications 74 (1922) · Zbl 0752.34039
[6] Tineo, A.: An iterative scheme for the N-competing species problem, J. differential equations 116, 1-15 (1995) · Zbl 0823.34048 · doi:10.1006/jdeq.1995.1026
[7] Murry, J. D.: Mathematical biology, (1989)
[8] Agarwal, R. P.: Difference equations and inequalities, (2000) · Zbl 0952.39001
[9] Chen, F. D.: Permanence for the discrete mutualism model with time delays, Math. comput. Modelling 47, 431-435 (2008) · Zbl 1148.39017 · doi:10.1016/j.mcm.2007.02.023
[10] Chen, F. D.: Permanence in a discrete Lotka--Volterra competition model with deviating arguments, Nonlinear anal. RWA 9, No. 5, 2150-2155 (2008) · Zbl 1156.39300 · doi:10.1016/j.nonrwa.2007.07.001
[11] Chen, F. D.; Wu, L. P.; Li, Z.: Permanence and global attractivity of the discrete gilpin--ayala type population model, Comput. math. Appl. 53, No. 8, 1214-1227 (2007) · Zbl 1127.92038 · doi:10.1016/j.camwa.2006.12.015
[12] Li, Z.; Chen, F. D.: Extinction in two dimensional discrete Lotka--Volterra competitive system with the effect of toxic substances, Dyn. contin. Discrete impuls. Syst. ser. B 15, No. 2, 165-178 (2008) · Zbl 1142.92044
[13] Wang, W. D.; Lu, Z. Y.: Global stability of discrete models of Lotka--Volterra type, Nonlinear anal. 35, 1019-1030 (1999) · Zbl 0919.92030 · doi:10.1016/S0362-546X(98)00112-6
[14] Wang, W. D.; Lu, Z. Y.: Global stability of discrete population models with delays and fluctuating environment, J. math. Anal. appl. 264, 147-167 (2001) · Zbl 1006.92025 · doi:10.1006/jmaa.2001.7666
[15] Zhou, Z.; Zou, X.: Stable periodic solutions in a discrete periodic logistic equation, Appl. math. Lett. 16, No. 2, 165-171 (2003) · Zbl 1049.39017 · doi:10.1016/S0893-9659(03)80027-7
[16] Chen, Y. M.; Zhou, Z.: Stable periodic solution of a discrete periodic Lotka--Volterra competition system, J. math. Anal. appl. 277, No. 1, 358-366 (2003) · Zbl 1019.39004 · doi:10.1016/S0022-247X(02)00611-X
[17] Yang, X. T.: Uniform persistence and periodic solutions for a discrete predator--prey system with delays, J. math. Anal. appl. 316, 161-177 (2006) · Zbl 1107.39017 · doi:10.1016/j.jmaa.2005.04.036
[18] Chen, F. D.: Permanence and global attractivity of a discrete multispecies Lotka--Volterra competition predator--prey systems, Appl. math. Comput. 182, 3-12 (2006) · Zbl 1113.92061 · doi:10.1016/j.amc.2006.03.026
[19] Gopalsamy, K.; Mohamad, S.: Canonical solutions and almost periodicity in a discrete logistic equation, Appl. math. Comput. 113, 305-323 (2000) · Zbl 1023.39012 · doi:10.1016/S0096-3003(99)00093-4
[20] Song, Y. H.: Almost periodic solutions of discrete Volterra equations, J. math. Anal. appl. 314, 174-194 (2006) · Zbl 1088.39007 · doi:10.1016/j.jmaa.2005.03.073
[21] Song, Y. H.; Tian, H. J.: Periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay, J. comput. Appl. math. 205, 859-870 (2007) · Zbl 1122.39007 · doi:10.1016/j.cam.2005.12.042
[22] Huang, Z. K.; Wang, X. H.; Gao, F.: The existence and global attractivity of almost periodic sequence solution of discrete-time neural networks, Phys. lett. A 350, 182-191 (2006) · Zbl 1195.34066 · doi:10.1016/j.physleta.2005.10.022
[23] Zhang, S. N.: Existence of almost periodic solution for difference systems, Ann. differential equations 16, No. 2, 184-206 (2000) · Zbl 0981.39003
[24] Fink, A. M.; Seifert, G.: Liapunov functions and almost periodic solutions for almost periodic systems, J. differential equations 5, 307-313 (1969) · Zbl 0167.07901 · doi:10.1016/0022-0396(69)90045-X
[25] Yuan, R.: The existence of almost periodic solutions of retarded differential equations with piecewise constant argument, Nonlinear anal. 48, 1013-1032 (2002) · Zbl 1015.34058 · doi:10.1016/S0362-546X(00)00231-5
[26] Samoilenko, A. M.; Perestyuk, N. A.: Impulsive differential equations, World scientific series on nonlinear science (1995) · Zbl 0837.34003
[27] Zhang, S. N.; Zheng, G.: Almost periodic solutions of delay difference systems, Appl. math. Comput. 131, 497-516 (2002) · Zbl 1029.39011 · doi:10.1016/S0096-3003(01)00165-5