×

Feedback control variables have no influence on the permanence of a discrete \(N\)-species cooperation system. (English) Zbl 1185.93072

Summary: A new set of sufficient conditions for the permanence of a discrete \(N\)-species cooperation system with delays and feedback controls are obtained. Our result shows that feedback control variables have no influence on the persistent property of the discrete cooperative system, thus improves and supplements the main result of F. D. Chen [Appl. Math. Comput. 186, No. 1, 23–29 (2007; Zbl 1113.93063)].

MSC:

93C55 Discrete-time control/observation systems
93B52 Feedback control

Citations:

Zbl 1113.93063
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] M. Fan, K. Wang, P. J. Y. Wong, and R. P. Agarwal, “Periodicity and stability in periodic n-species Lotka-Volterra competition system with feedback controls and deviating arguments,” Acta Mathematica Sinica, vol. 19, no. 4, pp. 801-822, 2003. · Zbl 1047.34080
[2] H.-F. Huo and W.-T. Li, “Positive periodic solutions of a class of delay differential system with feedback control,” Applied Mathematics and Computation, vol. 148, no. 1, pp. 35-46, 2004. · Zbl 1057.34093
[3] F. Chen, “Permanence of a discrete N-species cooperation system with time delays and feedback controls,” Applied Mathematics and Computation, vol. 186, no. 1, pp. 23-29, 2007. · Zbl 1113.93063
[4] Y.-H. Fan and L.-L. Wang, “Permanence for a discrete model with feedback control and delay,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 945109, 8 pages, 2008. · Zbl 1163.39011
[5] L. Wang and M. Q. Wang, Ordinary Difference Equation, Xinjiang University Press, Xinjiang, China, 1991. · Zbl 0734.34024
[6] Z. Zhou and X. Zou, “Stable periodic solutions in a discrete periodic logistic equation,” Applied Mathematics Letters, vol. 16, no. 2, pp. 165-171, 2003. · Zbl 1049.39017
[7] F. Chen, “Permanence for the discrete mutualism model with time delays,” Mathematical and Computer Modelling, vol. 47, no. 3-4, pp. 431-435, 2008. · Zbl 1148.39017
[8] K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, vol. 74 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992. · Zbl 0752.34039
[9] F. Chen, X. Liao, and Z. Huang, “The dynamic behavior of N-species cooperation system with continuous time delays and feedback controls,” Applied Mathematics and Computation, vol. 181, no. 2, pp. 803-815, 2006. · Zbl 1102.93021
[10] P. Weng, “Existence and global stability of positive periodic solution of periodic integrodifferential systems with feedback controls,” Computers & Mathematics with Applications, vol. 40, no. 6-7, pp. 747-759, 2000. · Zbl 0962.45003
[11] Y. Xiao, S. Tang, and J. Chen, “Permanence and periodic solution in competitive system with feedback controls,” Mathematical and Computer Modelling, vol. 27, no. 6, pp. 33-37, 1998. · Zbl 0896.92032
[12] K. Gopalsamy and P. X. Weng, “Feedback regulation of logistic growth,” International Journal of Mathematics and Mathematical Sciences, vol. 16, no. 1, pp. 177-192, 1993. · Zbl 0765.34058
[13] F. Chen, “Global asymptotic stability in n-species non-autonomous Lotka-Volterra competitive systems with infinite delays and feedback control,” Applied Mathematics and Computation, vol. 170, no. 2, pp. 1452-1468, 2005. · Zbl 1081.92038
[14] F. Yin and Y. 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
[15] F. Chen, “Permanence in nonautonomous multi-species predator-prey system with feedback controls,” Applied Mathematics and Computation, vol. 173, no. 2, pp. 694-709, 2006. · Zbl 1087.92059
[16] F. Chen, “Permanence for the discrete mutualism model with time delays,” Mathematical and Computer Modelling, vol. 47, no. 3-4, pp. 431-435, 2008. · Zbl 1148.39017
[17] X. Liao, S. Zhou, and Y. Chen, “Permanence and global stability in a discrete n-species competition system with feedback controls,” Nonlinear Analysis: Real World Applications, vol. 9, no. 4, pp. 1661-1671, 2008. · Zbl 1154.34352
[18] S. Lu, “On the existence of positive periodic solutions to a Lotka Volterra cooperative population model with multiple delays,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 6, pp. 1746-1753, 2008. · Zbl 1139.34317
[19] Z. Liu, R. Tan, Y. Chen, and L. Chen, “On the stable periodic solutions of a delayed two-species model of facultative mutualism,” Applied Mathematics and Computation, vol. 196, no. 1, pp. 105-117, 2008. · Zbl 1143.34054
[20] Z. Liu and L. Chen, “Periodic solutions of a discrete time nonautonomous two-species mutualistic system with delays,” Advances in Complex Systems, vol. 9, no. 1-2, pp. 87-98, 2006. · Zbl 1107.92053
[21] Y. Li and H. Zhang, “Existence of periodic solutions for a periodic mutualism model on time scales,” Journal of Mathematical Analysis and Applications, vol. 343, no. 2, pp. 818-825, 2008. · Zbl 1146.34326
[22] H. Wu, Y. Xia, and M. Lin, “Existence of positive periodic solution of mutualism system with several delays,” Chaos, Solitons & Fractals, vol. 36, no. 2, pp. 487-493, 2008. · Zbl 1156.34350
[23] Y. Xia, J. Cao, and S. S. Cheng, “Periodic solutions for a Lotka-Volterra mutualism system with several delays,” Applied Mathematical Modelling, vol. 31, no. 9, pp. 1960-1969, 2007. · Zbl 1167.34343
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.