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)
Positive periodic solution for a neutral logarithmic population model with feedback control. (English) Zbl 1214.92059
Summary: A neutral delay logarithmic population model with feedback control is studied. By using the abstract continuous theorem of k-set contractive operators, some new results on the existence of positive periodic solutions are obtained. After that, by constructing a suitable Lyapunov functional, a set of easily applicable criteria is established for the global asymptotic stability of positive periodic solutions.
MSC:
92D25Population dynamics (general)
93B25Algebraic theory of control systems
34C25Periodic solutions of ODE
34D23Global stability of ODE
34D05Asymptotic stability of ODE
References:
[1]Chen, F. D.: Periodic solutions and almost periodic solutions of a neutral multispecies logarithmic population model, Appl. math. Comput. 176, 431-441 (2006) · Zbl 1089.92039 · doi:10.1016/j.amc.2005.09.032
[2]Fan, M.; Wong, P. J. Y.; Agarwal, Ravi P.: Periodicity and stability in periodic n-species Lotka – Volterra competition system with feedback controls and deviating arguments, Acta. math. Sin. 19, No. 4, 801-822 (2003) · Zbl 1047.34080 · doi:10.1007/s10114-003-0311-1
[3]Gopalsamy, K.: Stability and oscillation in delay differential equations of population dynamics, Mathematics and its applications 74 (1992) · Zbl 0752.34039
[4]Gaines, R. E.; Mawhin, J. L.: Lecture notes in mathematics, (1977)
[5]Kirlinger, G.: Permanence in Lotka – Volterra equations linked prey-predator systems, Math. biosci. 82, 165-169 (1986) · Zbl 0607.92022 · doi:10.1016/0025-5564(86)90136-7
[6]Lu, S. P.; Ge, W. G.: Existence of positive periodic solutions for neutral logarithmic population model with multiple delays, J. comput. Appl. math. 166, No. 2, 371-383 (2004) · Zbl 1061.34053 · doi:10.1016/j.cam.2003.08.033
[7]Lu, S. P.; Ge, W. G.: Existence of positive periodic solutions for neutral population model with multiple delays, Appl. math. Comput 153, 885-902 (2004) · Zbl 1042.92026 · doi:10.1016/S0096-3003(03)00685-4
[8]Li, Y. K.: Attractivity of a positive periodic solution for all other positive solution in a delay population model, Appl. math. -JCU. 12, No. 3, 279-282 (1997) · Zbl 0883.92023
[9]Li, Y. K.: On a periodic neutral delay logarithmic population model, J. syst. Sci. math. Sci. 19, No. 1, 34-38 (1999) · Zbl 0953.92025
[10]Liu, Z. D.; Mao, Y. P.: Existence theorem for periodic solutions of higher order nonlinear differential equations, J. math. Anal. appl. 216, 481-490 (1997) · Zbl 0892.34040 · doi:10.1006/jmaa.1997.5669
[11]Petryshyn, W. V.; Yu, Z. S.: Existence theorems for higher order nonlinear periodic boundary value problems, Nonlinear anal. 6, No. 9, 943-969 (1982) · Zbl 0525.34015 · doi:10.1016/0362-546X(82)90013-X
[12]Wang, C. Z.; Shi, J. L.: Periodic solution for a delay multispecies logarithmic population model with feedback control, Appl. math. Comput 193, 257-265 (2007) · Zbl 1193.34144 · doi:10.1016/j.amc.2007.03.049
[13]Wang, Q.; Wang, Y.; Dai, B. X.: Existence and uniqueness of positive periodic solutions for a neutral logarithmic population model, Appl. math. Comput. 213, 137-147 (2009) · Zbl 1177.34093 · doi:10.1016/j.amc.2009.03.028
[14]Wang, Q.; Zhang, H. Y.; Wang, Y.: Existence and stability of positive almost periodic solutions and periodic solutions for a logarithmic population model, Nonlinear anal. 72, 4384-4389 (2010) · Zbl 1194.34153 · doi:10.1016/j.na.2010.01.001
[15]Zhou, Y. G.; Tang, X. H.: On existence of periodic solutions of Rayleigh equation of retarded type, J. comput. Appl. math. 203, 1-5 (2007) · Zbl 1115.34067 · doi:10.1016/j.cam.2006.03.002