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Positive periodic solutions of a class of delay differential system with feedback control. (English) Zbl 1057.34093
The authors present several sufficient conditions for guaranteeing the global existence of positive periodic solutions for a delay differential system with feedback control by using the continuation theorem given by Gaines and Mawhin and coincidence degree theory. In addition, the obtained results can be applied to some special delay population models.

34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
Full Text: DOI
[1] H.F. Huo, W.T. Li, Periodic solution of a periodic two-species competition model with delays, Int. J. Appl. Math., in press · Zbl 1043.34074
[2] Huo, H. F.; Li, W. T.; Cheng, S. S.: Periodic solutions of two-species diffusion models with continuous time delays. Demonstratio Mathematica 35, No. 2, 432-446 (2002) · Zbl 1013.92035
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[10] Yang, F.; Jiang, D. Q.: Existence and global attractivity of positive periodic solution of a logistic growth system with feedback control and deviating arguments. Ann. diff. Eqs. 17, No. 4, 377-384 (2001) · Zbl 1004.34030
[11] Fan, M.; Wang, K.: Periodicity in a delayed ratio-dependent predator--prey system. J. math. Anal. appl. 262, 179-190 (2001) · Zbl 0994.34058
[12] Li, Y. K.: Periodic solutions of a periodic delay predator-prey system. Proc. am. Math. soc. 127, 1331-1335 (1999) · Zbl 0917.34057
[13] Li, Y. K.; Kuang, Y.: Periodic solutions of periodic delay Lotka--Volterra equations and systems. J. math. Anal. appl. 255, 260-280 (2001) · Zbl 1024.34062
[14] Gaines, R. E.; Mawhin, J. L.: Coincidence degree and nonlinear differential equations. (1977) · Zbl 0339.47031
[15] Li, Y. K.: Existence and global attractivity of a positive periodic solution of a class of delay differential equation. Sci. China (Ser. A) 41, No. 3, 273-284 (1998) · Zbl 0955.34057