Feedback control variables have no influence on the permanence of a discrete \(n\)-species Schoener competition system with time delays. (English) Zbl 1205.93053
Summary: We consider a discrete \(n\)-species Schoener competition system with time delays and feedback controls. By using difference inequality theory, a set of conditions which guarantee the permanence of system is obtained. The results indicate that feedback control variables have no influence on the persistent property of the system. Numerical simulations show the feasibility of our results.
Keywords:
discrete \(n\)-species Schoener competition system; feedback controls; permanence of systemReferences:
| [1] | Q. M. Liu, R. Xu, and W. G. Wang, “Global asymptotic stability of Schoener’s competitive model with delays,” Journal of Biomathematics, vol. 21, no. 1, pp. 147-152, 2006. · Zbl 1127.92311 |
| [2] | G.-L. Chen, R. Xu, and Q.-M. Liu, “Periodic solutions of a competitive model with distributed time delays,” Journal of Biomathematics, vol. 19, no. 4, pp. 385-394, 2004 (Chinese). · Zbl 1115.92054 |
| [3] | Z. H. Lu and L. S. Chen, “Analysis on a periodic Schoener model,” Acata Mathematica Scientia, vol. 12, no. 7, supplement, pp. 105-109, 1992. |
| [4] | H. Xiang, K. M. Yan, and B. Y. Wang, “Positive periodic solutions for discrete Schoner competitive models,” Journal of Lanzhou University of Technology, vol. 31, no. 5, pp. 125-128, 2005 (Chinese). · Zbl 1089.39501 |
| [5] | L. Wu, F. Chen, and Z. Li, “Permanence and global attractivity of a discrete Schoener’s competition model with delays,” Mathematical and Computer Modelling, vol. 49, no. 7-8, pp. 1607-1617, 2009. · Zbl 1165.39302 · doi:10.1016/j.mcm.2008.06.004 |
| [6] | Z. Li and F. Chen, “Extinction in two dimensional discrete Lotka-Volterra competitive system with the effect of toxic substances,” Dynamics of Continuous, Discrete & Impulsive Systems. Series B, vol. 15, no. 2, pp. 165-178, 2008. · Zbl 1142.92044 |
| [7] | Y. Chen and Z. Zhou, “Stable periodic solution of a discrete periodic Lotka-Volterra competition system,” Journal of Mathematical Analysis and Applications, vol. 277, no. 1, pp. 358-366, 2003. · Zbl 1019.39004 · doi:10.1016/S0022-247X(02)00611-X |
| [8] | 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 · doi:10.1016/S0893-9659(03)80027-7 |
| [9] | Y. Muroya, “Persistence and global stability in discrete models of Lotka-Volterra type,” Journal of Mathematical Analysis and Applications, vol. 330, no. 1, pp. 24-33, 2007. · Zbl 1124.39011 · doi:10.1016/j.jmaa.2006.07.070 |
| [10] | W. Wang, G. Mulone, F. Salemi, and V. Salone, “Global stability of discrete population models with time delays and fluctuating environment,” Journal of Mathematical Analysis and Applications, vol. 264, no. 1, pp. 147-167, 2001. · Zbl 1006.92025 · doi:10.1006/jmaa.2001.7666 |
| [11] | F. Chen, “Permanence and global attractivity of a discrete multispecies Lotka-Volterra competition predator-prey systems,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 3-12, 2006. · Zbl 1113.92061 · doi:10.1016/j.amc.2006.03.026 |
| [12] | 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 · doi:10.1016/j.mcm.2007.02.023 |
| [13] | 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 · doi:10.1142/S1793524508000369 |
| [14] | 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 · doi:10.1016/S0096-3003(02)00824-X |
| [15] | X. Li and W. Yang, “Permanence of a discrete n-species Schoener competition system with time delays and feedback controls,” Advances in Difference Equations, vol. 2009, Article ID 515706, 10 pages, 2009. · Zbl 1175.93090 · doi:10.1155/2009/515706 |
| [16] | 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 · doi:10.1016/j.amc.2005.04.047 |
| [17] | 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 · doi:10.1016/j.amc.2006.07.084 |
| [18] | L. Chen, L. Chen, and Z. Li, “Permanence of a delayed discrete mutualism model with feedback controls,” Mathematical and Computer Modelling, vol. 50, no. 7-8, pp. 1083-1089, 2009. · Zbl 1185.93050 · doi:10.1016/j.mcm.2009.02.015 |
| [19] | F. Chen, “Positive periodic solutions of neutral Lotka-Volterra system with feedback control,” Applied Mathematics and Computation, vol. 162, no. 3, pp. 1279-1302, 2005. · Zbl 1125.93031 · doi:10.1016/j.amc.2004.03.009 |
| [20] | 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 · doi:10.1016/j.amc.2006.02.007 |
| [21] | L. Chen, X. Xie, and L. Chen, “Feedback control variables have no influence on the permanence of a discrete N-species cooperation system,” Discrete Dynamics in Nature and Society, vol. 2009, Article ID 306425, 10 pages, 2009. · Zbl 1185.93072 · doi:10.1155/2009/306425 |
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.
