zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Periodic solution for a delay multispecies logarithmic population model with feedback control. (English) Zbl 1193.34144
Summary: A delay multispecies Logarithmic population model with feedback control is studied. By using the contraction mapping principle as well as a new transformation, some new results on the existence and uniqueness of the periodic solution are obtained; After that, by constructing a suitable Lyapunov functional, a set of easily applicable criteria is established for the global asymptotically stability of the periodic solution.

MSC:
34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
93B52Feedback control
WorldCat.org
Full Text: DOI
References:
[1] Liu, Z. J.: Positive periodic solutions for delay multispecies logrithmic population model. Journal of engineering mathematics 19, No. 4, 11-16 (2002) · Zbl 1041.34059
[2] Gopalsamy, K.: Stability and oscillation in delay differential equations of population dynamics. Mathematics and its applications 74 (1992) · Zbl 0752.34039
[3] Li, Y. K.: Attractivity of a positive periodic solution for all other positive solution in a delay population model. Applied mathematics-JCU 12, No. 3, 279-282 (1997) · Zbl 0883.92023
[4] Kirlinger, G.: Permanence in Lotka -- Volterra equations linked prey -- predator systems. Mathematical biosciences 82, 165-169 (1986) · Zbl 0607.92022
[5] Chen, F. D.: Positive periodic solutions of state-dependent delay logarithm population model. Journal of fuzhou university 31, No. 3, 1-4 (2003)
[6] Chen, F. D.: Periodic solutions and almost periodic solutions of a neutral multispecies logarithmic population model. Applied mathematics and computation. 176, No. 2, 431-441 (2006) · Zbl 1089.92039
[7] Chen, F. D.: Periodic solutions and almost periodic solutions for a delay multispecies logarithmic population model. Applied mathematics and computation. 171, No. 2, 760-770 (2005) · Zbl 1089.92038
[8] Gaines, R. E.; Mawhin, J. L.: Coincidence degree and nonlinear differential equations [M]. (1977) · Zbl 0339.47031
[9] Chen, F. D.; Sun, D. X.; Shi, J. L.: Existence and uniqueness of periodic solutions of a kind of integro-differential equations. Acta Mathematica sinica (Chinese series) 47, No. 5, 973-984 (2004) · Zbl 1124.34043
[10] Xie, H. Q.; Wang, Q. Y.: Exponential stability and periodic solution for cellular neural networks with time delay. Journal of huaqiao university 25, No. 1, 22-26 (2004) · Zbl 1228.34117
[11] Fan, M.; Wong, Patrica J. Y.; Agarwal, Ravi P.: Periodicity and stability in periodic n-species Lotka -- Volterra competition system with feedback controls and deviating arguments. Acta mathematics sinica 19, No. 4, 801-822 (2003) · Zbl 1047.34080
[12] Chen, F. D.; Lin, F. X.; Chen, X. X.: Sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control. Applied mathematics and computation 158, No. 1, 45-68 (2004) · Zbl 1096.93017
[13] Chen, F. D.: Positive periodic solutions of neutral Lotka -- Volterra system with feedback control. Applied mathematics and computation 162, No. 3, 1279-1302 (2005) · Zbl 1125.93031
[14] Weng, P. X.: Global attractivity in a periodic competition system with feedback controls. Acta applicandae mathematicae 12, 11-21 (1996) · Zbl 0859.34061
[15] Weng, P. X.: Existence and global stability of positive periodic solution of periodic integro-differential systems with feedback controls. Computers and mathematics with applications 40, 747-759 (2000) · Zbl 0962.45003
[16] Weng, P. X.; Jiang, D. Q.: Existence and global stability of positive periodic solution of n-species periodic Lotka -- Volterra competition systems with feedback controls and deviating arguments. Far east journal mathematical science 7, No. 1, 45-65 (2002) · Zbl 1043.34075
[17] Xiao, Y. N.; Tang, S. Y.; Chen, J. F.: Permanence and periodic solution in competition system with feedback controls. Mathematical and computer modelling 27, No. 6, 33-37 (1998) · Zbl 0896.92032
[18] Gopalsamy, K.; Weng, P. X.: Feedback regulation of logistic growth. International journal of mathematical science 16, No. 1, 177-192 (1993) · Zbl 0765.34058
[19] Yang, F.; Jiang, D. Q.: Existence and global attractivity of positive periodic solution of a logistic growth system with feedback control and deviating arguments. Annals of differential equations 17, No. 4, 337-384 (2001) · Zbl 1004.34030
[20] Li, X. Y.; Fan, M.; Wang, K.: Positive periodic solution of single species model with feedback regulation and infinite delay. Applied mathematics journal of chinese university series 17, No. 1, 13-21 (2002)
[21] Huo, H.; Li, W.: Positive periodic solutions of a class of delay differential system with feedback control. Applied mathematics and computation 148, No. 1, 35-46 (2004) · Zbl 1057.34093
[22] Xia, Y. H.; Cao, J. D.; Zhang, H. Y.; Chen, F. D.: Almost periodic solutions of n-species competitive system with feedback controls. Journal of mathematical analysis and applications 294, No. 2, 503-522 (2004) · Zbl 1053.34040
[23] Chen, F. D.: Global asymptotic stability in n-species non-autonomous Lotka -- Volterra competitive systems with infinite delays and feedback control. Applied mathematics and computation 170, No. 2, 1452-1468 (2005) · Zbl 1081.92038
[24] Chen, F. D.: The permanence and global attractivity of Lotka -- Volterra competition system with feedback controls. Nonlinear analysis: real world applications 7, No. 1, 133-143 (2006) · Zbl 1103.34038
[25] Chen, F. D.: Permanence in nonautonomous multi-species predator -- prey system with feedback controls. Applied mathematics and computation 173, No. 2, 694-709 (2006) · Zbl 1087.92059
[26] Chen, F. D.: Permanence of a discrete n-species cooperation system with time delays and feedback controls. Applied mathematics and computation 186, No. 1, 23-29 (2007) · Zbl 1113.93063
[27] Chen, F. D.: On the periodic solutions of periodic multi-species Kolmogorov type competitive system with delays and feedback controls. Applied mathematics and computation 180, No. 1, 366-373 (2006) · Zbl 1113.34050
[28] Chen, F. D.; Li, Z.; Huang, Y. J.: Note on the permanence of a competitive system with infinite delay and feedback controls. Nonlinear analysis: real world applications 8, No. 2, 680-687 (2007) · Zbl 1152.34366
[29] Kuang, Y.: Global stability in delayed nonautonomous Lotka -- Volterra type systems without saturated equlibria. Differential integral equations 9, No. 3, 557-567 (1996) · Zbl 0843.34077