Existence and global attractivity of positive periodic solutions of functional differential equations with feedback control

Journal of Computational and Applied Mathematics

Volumn 180, Issue 2, 2005, Pages 293-309

  Li, Wan Tong ^a   Wang, Lin Lin ^b  

^a LANZHOU UNIVERSITY   (China)

^b TIANJIN UNIVERSITY   (China)

Author keywords

Delay differential equations; Feedback control; Global attractivity; Positive periodic solutions

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FEEDBACK CONTROL; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; SET THEORY;

DELAY DIFFERENTIAL EQUATIONS; GLOBAL ATTRACTIVITY; POSITIVE PERIODIC SOLUTIONS;

DIFFERENTIAL EQUATIONS;

EID: 18644369681     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.11.002     Document Type: Article

References (38)

1. I. Barbalat Systems d'equations differentielle d'oscillations nonlineaires Rev. Roumaine Math. Pures Appl. 4 1959 267-270
2. K. Deimling Nonlinear Functional Analysis 1985 Springer New York
3. R.E. Gaines J.L. Mawhin Coincidence Degree and Nonlinear Differential Equations 1977 Springer Berlin
4. K. Gopalsamy Stability and Oscillations in Delay Differential Equations of Population Dynamics 1992 Kluwer Academic Publishers Dordrecht
5. K. Gopalsamy M.R.S. Kulenović G. Ladas Environmental periodicity and time delays in a "food-limited"; population model J. Math. Anal. Appl. 147 1990 545-555
6. K. Gopalsamy B.S. Lalli Oscillatory and asymptotic behavior of a multiplicative delay logistic equation Dynamic Stability Systems 7 1992 35-42
7. K. Gopalsamy P.X. Weng Feedback regulation of logistic growth Internat. J. Math. Sci. 1 1993 177-192
8. S.R. Grace I. Györi B.S. Lalli Necessary and sufficient conditions for the oscillations of a multiplicative delay logistic equation Quart. Appl. Math. 53 1995 69-79
9. J.R. Greaf C. Qian P.W. Spikes Oscillation and global attractivity in a periodic delay equation Canad. Math. Bull. 38 1996 275-283
10. J.R. Greaf C. Qian B. Zhang Asymptotic behavior of solutions of differential equations with variable delays Proc. London Math. Soc. 81 2000 72-92
11. I. Györi G. Ladas Oscillation Theorem of Delay Differential Equations with Applications 1991 Clarendon Press Oxford
12. H.F. Huo W.T. Li Positive periodic solutions of delay differential systems with feedback control Appl. Math. Comput. 148 2004 35-46
13. D.Q. Jiang J. Wei B. Zhang Positive periodic solutions of functional differential equations and population models Electron. J. Differential Equations 71 2002 1-13
14. M.A. Krasnoselskii Positive Solutions of Operator Equations 1964 Gorninggen Noordhoff
15. Y. Kuang Delay Differential Equations with Application in Population Dynamics 1993 Academic Press New York
16. G.S. Ladde V. Lakshmikantham B.Z. Zhang Oscillation Theory of Differential Equations with Deviating Arguments 1987 Marcel Dekker New York
17. B.S. Lalli J.S. Yu M.P. Chen Feedback regulation of a logistic growth Dynam. Systems Appl. 5 1996 117-124
18. B.S. Lalli B.G. Zhang On a periodic delay population model Quart. Appl. Math. 52 1994 35-42
19. J. LaSalle S. Lefschetz Stability by Lyapunov's Direct Method 1961 Academic Press New York
20. S. Lefschetz Stability of Nonlinear Control Systems 1965 Academic Press New York
21. Y.K. Li Existence and global attractivity of a positive periodic solution of a class of delay differential equation Sci. China Ser. A 41 1998 273-284
22. L. Liao Feedback regulation of a logistic growth with variable coefficients J. Math. Anal. Appl. 259 2001 489-500
23. M.C. Mackey L. Glass Oscillation and chaos in physiological control system Science 197 1977 287-289
24. A.J. Nicholson The balance of animal population J. Animal Ecol. 2 1933 132-178
25. R.M. Nisbet W.S.C. Gurney Population dynamics in a periodically varying environment J. Theoret. Biol. 56 1976 459-475
26. E.R. Pianka Evolutionary Ecology 1974 Harper and Row New York
27. C. Qian Global attractivity in nonlinear delay differential equations J. Math. Anal. Appl. 197 1996 529-547
28. G. Rosen Time delays produced by essential nonlinearity in population growth models Bull. Math. Biol. 28 1987 253-256
29. S.H. Saker Oscillation and global attractivity in a periodic delay hematopoiesis model Appl. Math. Comput. 136 2003 241-250
30. S.H. Saker S. Agarwal Oscillation and global attractivity in a periodic Nichlson's blowflies model Math. Comput. Modelling 35 2002 719-731
31. S.H. Saker S. Agarwal Oscillation and global attractivity in a nonlinear delay periodic model of population dynamics Appl. Anal. 81 2002 787-799
32. S.H. Saker, S. Agarwal, Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics, Comput. Math. Appl. 44 (2002) 5-6, 623-632.
33. S.H. Saker, S. Agarwal, Oscillation and global attractivity of a periodic survival red blood cells model, Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, in press.
34. D. Schley S.A. Gourley Linear stability criteria for population models with periodic perturbed delays J. Math. Biol. 40 2000 500-524
35. X. Tang X. Zou A 3 / 2 stability result for a regulated logistic growth model Discrete Contin. Dynam. Systems Ser. B 2 2002 265-278
36. J. Yan Q. Feng Global attractivity and oscillation in a nonlinear delay equation Nonlinear Analysis-TMA 43 2001 101-108
37. F. Yang D.Q. Jiang Existence and global attractivity of positive periodic solution of a logistic growth system with feedback control and deviating arguments Ann. Differential Equations 17 2001 377-384
38. B.G. Zhang K. Gopalsamy Global attractivity and oscillations in a periodic delay-logistic equation J. Math. Anal. Appl. 150 1990 274-283