Permanence and almost periodic sequence solution for a discrete delay logistic equation with feedback control

Nonlinear Analysis: Real World Applications

Volumn 12, Issue 3, 2011, Pages 1850-1864

  Li, Yongkun ^a   Zhang, Tianwei ^a  

^a YUNNAN UNIVERSITY   (China)

Author keywords

Almost periodic solution; Delay logistic equation; Discrete; Permanence

Indexed keywords

ALMOST PERIODIC; ALMOST PERIODIC SOLUTIONS; DELAY LOGISTIC EQUATION; DISCRETE; DISCRETE DELAY; LOGISTIC EQUATIONS; LYAPUNOV FUNCTIONALS; PERMANENCE; SUFFICIENT CONDITIONS;

FEEDBACK CONTROL; PROBLEM SOLVING;

TIME DELAY;

EID: 79952619723     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2010.12.001     Document Type: Article

References (32)

1. B.D. Coleman Nonautonomous logistic equations as models of the adjustment of populations to environmental changes Math. Biosci. 45 1979 159 173 (Pubitemid 9248083)
2. B.D. Coleman, Y.H. Hsieh, and G.P. Knowles On the optimal choice of r for a population in a periodic environment Math. Biosci. 46 1979 71 85 (Pubitemid 10221393)
3. K. Gopalsamy, and X.Z. He Dynamics of an almost periodic logistic integrodifferential equation Methods Appl. Anal. 2 1995 38 66
4. M.E. Clark, and L.J. Gross Periodic solutions to nonautonomous difference equations Math. Biosci. 102 1990 105 119
5. K. Gopalsamy, and S. Mohamad Canonical solutions and almost periodicity in a discrete logistic equation Appl. Math. Comput. 113 23 2000 305 323
6. D. Cheban, and C. Mammana Invariant manifolds, global attractors and almost periodic solutions of nonautonomous difference equations Nonlinear Anal. 56 4 2004 465 484
7. S.N. Zhang Existence of almost periodic solution for difference systems Ann. Differential Equations 16 2 2000 184 206
8. S.N. Zhang, and G. Zheng Almost periodic solutions of delay difference systems Appl. Math. Comput. 131 2002 497 516 (Pubitemid 34813502)
9. Z. Zhou, and X.F. Zou Stable periodic solution in a discrete periodic logistic equation Appl. Math. Lett. 16 2003 165 171
10. Z. Li, and F.D. Chen Almost periodic solutions of a discrete almost periodic logistic equation Math. Comput. Modelling 50 2009 254 259
11. J.M. Cushing Integrodifferential Equations and Delay Models in Population Dynamics Lecture Notes in Biomathematics vol. 20 1977 Springer-Verlag Heidelberg
12. K. Gopalsamy Stability and Oscillations in Delay Differential Equations of Population Dynamics Mathematics and its Applications vol. 74 1992 Kluwer Academic Pub. Dordrecht
13. K. Kuang Delay Differential Equations with Applications in Population Dynamics 1993 Academic Press New York
14. N. Macdonald Time Lags in Biological Models Lecture Notes in Biomathematics vol. 27 1978 Springer-Verlag Heidelberg
15. H.R. Sun, and W.T. Li Qualitative analysis of a discrete logistic equation with several delays Appl. Math. Comput. 147 2004 515 525
16. Y. Muroya Global attractivity for discrete models of nonautonomous logistic equations Comput. Math. Appl. 53 2007 1059 1073 (Pubitemid 46727001)
17. C.Y. Niu, and X.X. Chen Almost periodic sequence solutions of a discrete LotkaVolterra competitive system with feedback control Nonlinear Anal. RWA 10 2009 3152 3161
18. N. Wiener Cybernetics: Or Control and Communication in the Animal and the Machine 1948 MIT Press Cambridge
19. L.S. Liao Feedback regulation of a logistic growth with variable coefficients J. Math. Anal. Appl. 259 2 2001 489 500
20. K. Gopalsamy, and P.X. Weng Feedback regulation of logistic growth Int. J. Math. Sci. 16 1 1993 177 192
21. P.X. Weng Global attractivity in a periodic competition system with feedback control Acta Appl. Math. 12 1996 11 21
22. B.S. Lalli, J.S. Yu, and M.P. Chen Feedback regulation of a logistic growth Dyn. Syst. Appl. 5 1996 117 124
23. H.F. Huo, and W.T. Li Positive periodic solutions of a class of delay differential system with feedback control Appl. Math. Comput. 148 1 2004 35 46
24. Y.K. Li Positive periodic solutions for neutral functional differential equations with distributed delays and feedback control Nonlinear Anal. RWA 9 2008 2214 2221
25. H.X. Hu, Z.D. Teng, and S.J. Gao Extinction in nonautonomous LotkaVolterra competitive system with pure-delays and feedback controls Nonlinear Anal. RWA 10 2009 2508 2520
26. O. Tagashira Permanent coexistence in chemostat models with delayed feedback control Nonlinear Anal. RWA 10 3 2009 1443 1452
27. L.L. Wang, and Y.H. Fan Permanence and existence of periodic solutions for a generalized system with feedback control Appl. Math. Comput. 216 2010 902 910
28. X.T. Yang Uniform persistence and periodic solutions for a discrete predatorprey system with delays J. Math. Anal. Appl. 316 2006 161 177
29. Y.H. Fan, and L.L. Wang Permanence for a discrete model with feedback control and delay Discrete Dyn. Nat. Soc. 2008 2008 8 pp. Article ID 945109
30. A.M. Fink, and G. Seifert Liapunov functions and almost periodic solutions for almost periodic systems J. Differential Equations 5 1969 307 313
31. R. Yuan The existence of almost periodic solutions of retarded differential equations with piecewise constant argument Nonlinear Anal. 48 2002 1013 1032 (Pubitemid 33149337)
32. R.P. Agarwal, M. Bohner, and P. ehk Half-linear dynamic equations Nonlinear Analysis and Applications to V. Lakshmikantham on his 80th Birthday vol. 1 2003 Kluwer Academic Publishers Dordrecht 1 57