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)
Almost periodic solutions of a discrete mutualism model with feedback controls. (English) Zbl 1185.92093
Summary: We consider a discrete mutualism model with feedback control. Assuming that the coefficients in the system are almost periodic sequences, we obtain the existence and uniqueness of the almost periodic solutions which are uniformly asymptotically stable.

MSC:
92D40Ecology
93B52Feedback control
34K14Almost and pseudo-periodic solutions of functional differential equations
37N25Dynamical systems in biology
34K20Stability theory of functional-differential equations
34K25Asymptotic theory of functional-differential equations
WorldCat.org
Full Text: DOI EuDML
References:
[1] C. L. Wolin and L. R. Lawlor, “Models of facultative mutualism: density effects,” The American Naturalist, vol. 114, pp. 843-862, 1984.
[2] B. S. Goh, “Stability in models of mutualism,” American Naturalist, vol. 113, pp. 216-275, 1979.
[3] Z. B. Zhang, “Mutualism or cooperation among competitors promotes coexistence and competitive ability,” Ecological Modelling, vol. 164, pp. 271-282, 2003.
[4] K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, vol. 74 of Mathematics and Its Applications, Kluwer Academic Publishers, Dodrecht, The Netherlands, 1992. · Zbl 0752.34039
[5] J. H. Vandermeer and D. H. Boucher, “Varieties of mutualistic interaction in population models,” Journal of Theoretical Biology, vol. 74, no. 4, pp. 549-558, 1978.
[6] D. H. Boucher, S. James, and K. H. Keeler, “The ecology of mutualism,” Annual Review of Ecology and Systematics, vol. 13, pp. 315-347, 1982.
[7] A. M. Dean, “A simple model of mutualism,” American Naturalist, vol. 121, no. 3, pp. 409-417, 1983. · doi:10.1086/284069
[8] L. Wolm and L. R. Lawlor, “Models of facultative mutualism Density effects,” American Naturalist, vol. 144, pp. 843-862, 1984.
[9] D. H. Boucher, The Biology of Mutualism Ecology and Evolution, Croom Helm, London, UK, 1985.
[10] R. P. Agarwal, Difference Equations and Inequalities: Theory, Methods and Applications, vol. 228 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2000. · Zbl 0952.39001
[11] J. D. Murray, Mathematical Biology, vol. 19 of Biomathematics, Springer, Berlin, Germany, 1989. · Zbl 0682.92001
[12] M. Fan and K. Wang, “Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system,” Mathematical and Computer Modelling, vol. 35, no. 9-10, pp. 951-961, 2002. · Zbl 1050.39022 · doi:10.1016/S0895-7177(02)00062-6
[13] X. Chen and C. Fengde, “Stable periodic solution of a discrete periodic Lotka-Volterra competition system with a feedback control,” Applied Mathematics and Computation, vol. 181, no. 2, pp. 1446-1454, 2006. · Zbl 1106.39003 · doi:10.1016/j.amc.2006.02.039
[14] F. Q. Yin and Y. K. Li, “Positive periodic solutions of a single species model with feedback regulation and distributed time delay,” Applied Mathematics and Computation, vol. 153, no. 2, pp. 475-484, 2004. · Zbl 1087.34051 · doi:10.1016/S0096-3003(03)00648-9
[15] G. Fan, Y. Li, and M. Qin, “The existence of positive periodic solutions for periodic feedback control systems with delays,” Zeitschrift fur Angewandte Mathematik und Mechanik, vol. 84, no. 6, pp. 425-430, 2004. · Zbl 1118.34328 · doi:10.1002/zamm.200310104
[16] L. F. Nie, J. G. Peng, and Z. D. Teng, “Permanence and stability in multi-species nonautonomous Lotka-Volterra competitive systems with delays and feedback controls,” Mathematical and Computer Modelling, vol. 49, pp. 295-306, 2009. · Zbl 1165.34373 · doi:10.1016/j.mcm.2008.05.004
[17] H. X. Hu, Z. D. Teng, and H. J. Jiang, “Permanence of the nonautonomous competitive systems with infinite delay and feedback controls,” Nonlinear Analysis: Real World Applications, vol. 10, no. 4, pp. 2420-2433, 2009. · Zbl 1163.45302 · doi:10.1016/j.nonrwa.2008.04.022
[18] X. X. Chen and F. D. Chen, “Almost-periodic solutions of a delay population equation with feedback control,” Nonlinear Analysis: Real World Applications, vol. 7, no. 4, pp. 559-571, 2006. · Zbl 1128.34045 · doi:10.1016/j.nonrwa.2005.03.017
[19] X. X. Chen, “Almost-periodic solutions of a delay population equation with feedback control,” Nonlinear Analysis: Real World Applications, vol. 8, pp. 62-72, 2007. · Zbl 1120.34054 · doi:10.1016/j.nonrwa.2005.05.007
[20] K. Gopalsamy, “Global asymptotic stability in an almost periodic Lotka-Volterra system,” Journal of the Australian Mathematical Society. Series B, vol. 27, pp. 346-360, 1986. · Zbl 0591.92022 · doi:10.1017/S0334270000004975
[21] C. Wang and J. Shi, “Positive almost periodic solutions of a class of Lotka-Volterra type competitive system with delays and feedback controls,” Applied Mathematics and Computation, vol. 193, no. 1, pp. 240-252, 2007. · Zbl 1193.34146 · doi:10.1016/j.amc.2007.03.048
[22] W. Qi and B. Dai, “Almost periodic solution for n-species Lotka-Volterra competitive system with delay and feedback controls,” Applied Mathematics and Computation, vol. 200, no. 1, pp. 133-146, 2008. · Zbl 1146.93021 · doi:10.1016/j.amc.2007.10.055
[23] D. Cheban and C. Mammana, “Invariant manifolds, global attractors and almost periodic solutions of nonautonomous difference equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 56, no. 4, pp. 465-484, 2004. · Zbl 1065.39026 · doi:10.1016/j.na.2003.09.009
[24] S. N. Zhang, “Existence of almost periodic solution for difference systems,” Annals of Differential Equations, vol. 16, no. 2, pp. 184-206, 2000. · Zbl 0981.39003