×

Permanence of the nonautonomous competitive systems with infinite delay and feedback controls. (English) Zbl 1163.45302

Summary: We study the permanence of a class of nonautonomous two-species Lotka-Volterra competitive systems with infinite delay and feedback controls. New results on the permanence of solutions are obtained. The corresponding results given in [F. Chen, Z. Li, Y. Huang, Note on the permanence of a competitive system with infinite delay and feedback controls, Nonlinear Anal. RWA 8 (2007) 680-687] are improved and extended.

MSC:

45D05 Volterra integral equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chen, F., Positive periodic solutions of neutral Lotka-Volterra system with feedback control, Appl. Math. Comput., 162, 1279-1302 (2005) · Zbl 1125.93031
[2] Chen, F., Global asymptotic stability in \(n\)-species nonautonomous Lotka-Volterra competitive systems with infinite delays and feedback control, Appl. Math. Comput., 170, 1452-1468 (2005) · Zbl 1081.92038
[3] Chen, F., The permanence and global attractivity of Lotka-Volterra competition system with feedback controls, Nonlinear Anal. RWA, 7, 133-143 (2006) · Zbl 1103.34038
[4] Chen, F., Global stability of a single species model with feedback control and distributed time delay, Appl. Math. Comput., 178, 474-479 (2006) · Zbl 1101.92035
[5] Chen, F., Permanence in nonautonomous multi-species predator-prey system with feedback controls, Appl. Math. Comput., 173, 694-709 (2006) · Zbl 1087.92059
[6] Chen, F., On the periodic solutions of periodic multi-species Kolmogorov type competitive system with delays and feedback controls, Appl. Math. Comput., 180, 366-373 (2006) · Zbl 1113.34050
[7] Chen, F.; Li, Z.; Huang, Y., Note on the permanence of a competitive system with infinite delay and feedback controls, Nonlinear Anal. RWA, 8, 680-687 (2007) · Zbl 1152.34366
[8] Chen, F.; Lin, F.; Chen, X., Sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control, Appl. Math. Comput., 158, 45-68 (2004) · Zbl 1096.93017
[9] Chen, X., Almost periodic solutions of nonlinear delay population equation with feedback control, Nonlinear Anal. RWA, 8, 62-72 (2007) · Zbl 1120.34054
[10] Chen, X.; Chen, F., Almost-periodic solutions of a delay population equation with feedback control, Nonlinear Anal. RWA, 7, 559-571 (2006) · Zbl 1128.34045
[11] Fan, M.; Wong, P. J.Y.; Agarwal, R. P., Periodicity and stability in Periodic \(n\)-species Lotka-Volterra competition system with feedback controls and deviating arguments, Acta Math. Sin. Engl. Ser., 19, 801-822 (2003) · Zbl 1047.34080
[12] Gopalsamy, K.; Weng, P., Global attractivity in a competition system with feedback controls, Comput. Math. Appl., 45, 665-676 (2003) · Zbl 1059.93111
[13] Huo, H.; Li, W., Positive periodic solutions of a class of delay differential system with feedback control, Appl. Math. Comput., 148, 35-46 (2004) · Zbl 1057.34093
[14] Li, W.; Wang, L., Existence and global attractivity of positive periodic solutions of functional differential equations with feedback control, J. Comput. Appl. Math., 180, 293-309 (2005) · Zbl 1069.34100
[15] Li, Y., Positive periodic solutions for a periodic neutral differential equation with feedback control, Nonlinear Anal. RWA, 6, 145-154 (2005) · Zbl 1092.34033
[16] Li, Y.; Liu, P.; Zhu, L., Positive periodic solution of a class of functional differential systems with feedback controls, Nonlinear Anal., 57, 655-666 (2004) · Zbl 1064.34049
[17] Li, Y.; Zhu, L., Positive periodic solutions for a class of higher-dimensional state-dependent delay functional differential equations with feedback control, Appl. Math. Comput., 159, 783-795 (2004) · Zbl 1161.34346
[18] Liao, L., Feedback regulation of a logistic growth with variable coefficients, J. Math. Anal. Appl., 259, 489-500 (2001) · Zbl 1003.34069
[19] Liu, P.; Li, Y., Multiple positive periodic solutions of nonlinear functional differential system with feedback control, J. Math. Anal. Appl., 288, 819-832 (2003) · Zbl 1045.34045
[20] Liu, G.; Yan, J., Positive periodic solutions for a neutral differential system with feedback control, Comput. Math. Appl., 52, 401-410 (2006) · Zbl 1141.34344
[21] Montes de Oca, F.; Vival, M., Extinction in a two dimensional Lotka-Volterra system with infinite delay, Nonlinear Anal. RWA, 7, 1042-1047 (2006) · Zbl 1122.34058
[22] Song, Y.; Yuan, S., Bifurcation analysis for a regulated logistic growth model, Appl. Math. Modelling, 31, 1729-1738 (2007) · Zbl 1167.34377
[23] Teng, Z., Permanence and stability in non-autonomous logistic systems with infinite delay, Dyn. Syst., 17, 187-202 (2002) · Zbl 1035.34086
[24] Teng, Z.; Chen, L., The positive periodic solutions of periodic Kolmogorov type systems with delays, Acta Math. Appl. Sin., 22, 446-456 (1999), (in Chinese) · Zbl 0976.34063
[25] Teng, Z.; Li, Z., Permanence and asymptotic behavior of the \(n\)-species nonautonomous Lotka-Volterra competitive systems, Comput. Math. Appl., 39, 107-116 (2000) · Zbl 0959.34039
[26] Teng, Z.; Li, Z.; Jiang, H., Permanence criteria in non-autonomous predator-prey Kolmogorov systems and its applications, Dyn. Syst., 19, 171-194 (2004) · Zbl 1066.34048
[27] Weng, P., Existence and global stability of positive periodic solution of periodic integro-differential systems with feedback controls, Comput. Math. Appl., 40, 747-759 (2000) · Zbl 0962.45003
[28] Weng, P.; Jiang, D., Existence and global stability of positive periodic of \(n\)-species periodic Lotka-Volterra competition system with feedback control and deviating arguments, Far East J. Math. Sci., FJMS, 7, 45-65 (2002) · Zbl 1043.34075
[29] Xia, Y.; Cao, J.; Zhang, H.; Chen, F., Almost periodic solutions of \(n\)-species competitive system with feedback controls, J. Math. Anal. Appl., 294, 503-522 (2004) · Zbl 1053.34040
[30] Xiao, Y.; Tang, S.; Chen, J., Permanence and periodic solution in competitive system with feedback controls, Math. Comput. Modelling, 27, 6, 33-37 (1998) · Zbl 0896.92032
[31] Yang, Z.; Zhou, Z., Periodic solutions of a class of neutral differential models with feedback control, Appl. Math. Comput., 189, 996-1009 (2007) · Zbl 1117.93033
[32] Yin, F.; Li, Y., Positive periodic solutions of a single species model with feedback regulation and distributed time delay, Appl. Math. Comput., 153, 475-484 (2004) · Zbl 1087.34051
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.