Feedback control has no influence on the persistent property of a single species discrete model with time delays

Gopalsamy, 1992 Fan, 2004, The existence of positive periodic solutions for periodic feedback control systems with delays, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, 84, 425, 10.1002/zamm.200310104 Chen, 2010, Note on the persistent property of a feedback control system with delays, Nonlinear Analysis: Real World Applications, 11, 1061, 10.1016/j.nonrwa.2009.01.045 Agarwal, 1997 Freedman, 1980 Murry, 1989 Gopalsamy, 1992 Yang, 2006, Uniform persistence and periodic solutions for a discrete predator–prey system with delays, Journal of Mathematical Analysis and Applications, 316, 161, 10.1016/j.jmaa.2005.04.036 Fan, 2004, Permanence for a delayed discrete ratio-dependent predator–prey system with Holling type functional response, Journal of Mathematical Analysis and Applications, 299, 357, 10.1016/j.jmaa.2004.02.061 Fan, 2002, Periodic solutions of a discrete time nonautonomous ratio-dependent predator–prey system, Mathematical and Computer Modelling, 35, 951, 10.1016/S0895-7177(02)00062-6 Fan, 2003, Periodicity and stability in periodic n-species Lotka–Volterra competition system with feedback controls and deviating arguments, Acta Mathematica Sinica, 19, 801, 10.1007/s10114-003-0311-1 Huo, 2004, Positive periodic solutions of a class of delay differential system with feedback control, Applied Mathematics and Computation, 148, 35, 10.1016/S0096-3003(02)00824-X Chen, 2006, The dynamic behavior of N-species cooperation system with continuous timedelays and feedback controls, Applied Mathematics and Computation, 181, 803, 10.1016/j.amc.2006.02.007 Chen, 2007, Permanence of a single species discrete model with feedback control and delay, Applied Mathematics Letters, 20, 729, 10.1016/j.aml.2006.08.023 Y.H. Fan, 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 p., doi:10.1155/2008/945109. Wang, 1991 Chen, 2006, Permanence and global attractivity of a discrete multispecies Lotka–Volterra competition predator–prey systems, Applied Mathematics and Computation, 182, 3, 10.1016/j.amc.2006.03.026