참고문헌
- J.D. Murray, Mathematical biology I: An introduction, Springer-Verlag, Berlin, 2002.
- R.H. Tan, Z.J. Liu and R.A. Cheke, Periodicity and stability in a single-species model governed by impulsive differential equation, Appl. Math. Modelling, 36 (2012) 1085-1094. https://doi.org/10.1016/j.apm.2011.07.056
- Y.K. Li., P. Liu and L.F. Zhu, Positive periodic solutions of a class of functional differential systems with feedback controls, Nonlinear Anal. 57 (2004) 655-666. https://doi.org/10.1016/j.na.2004.03.006
- P. Weng, Existence and global stability of positive periodic solution of periodic integrodifferential systems with feedback controls, Comput. Math. Appl. 40 (2000) 747-759. https://doi.org/10.1016/S0898-1221(00)00193-0
- Y.K. Li and T.W. Zhang, Permanence of a discrete n-species cooperation system with time-varying delays and feedback controls, Math. Comput. Modelling 53 (2011) 1320-1330. https://doi.org/10.1016/j.mcm.2010.12.018
- F.D. Chen, F.X. Lin and X.X. Chen, Sufficient conditions for the existence of positive periodic solutions of a class of neutral delay models with feedback control, Appl. Math. Comput. 158 (2004) 45-68. https://doi.org/10.1016/j.amc.2003.08.063
- Y. Xia, J. Cao, H. Zhang and F. Chen, Almost periodic solutions of n-species competitive system with feedback controls, J. Math. Anal. Appl. 294 (2004) 503-522. https://doi.org/10.1016/j.jmaa.2004.02.025
- R.P. Agarwal, Difference Equations and Inequalities: Theory Methods and Applications Monographs and Textbooks in Pure and Applied Mathematics, 228, Marcel Dekker, New York, 2000.
- J.D. Murray, Mathematical Biology, Springer-Verlag, New York, 1989.
- X.Y. Liao and S.S. Cheng, Convergent and divergent solutions of a discrete nonautonomous Lotka-Volterra model, Tamkang J. Math. 36 (2005) 337-344.
- X.Y. Liao, W.T. Li and Y.N. Raffoul, Boundedness in nonlinear functional difference equation via non-negative definite Lyapunov functionals with applications to Volterra discrete systems, Nonlinear Stud. 13 (2006) 1-13.
- X.Y. Liao, S.F. Zhou, Z. Ouyang, On a stoichiometric two predators on one prey discrete model, Appl. Math. Lett. 20 (2007) 272-278. https://doi.org/10.1016/j.aml.2006.04.007
- Y.K. Li and T.W. Zhang, Permanence and almost periodic sequence solution for a discrete delay logistic equation with feedback control, Nonlinear Anal. Real World Appl. 12 (2011) 1850-1864. https://doi.org/10.1016/j.nonrwa.2010.12.001
- Y.K. Li, T.W. Zhang and Y. Ye, On the existence and stability of a unique almost periodic sequence solution in discrete predator-prey models with time delays, Appl. Math. Model. 35 (2011) 5448-5459. https://doi.org/10.1016/j.apm.2011.04.034
- X. Liao, S. Zhou and Y. Chen, Permanence and global stability in a discrete n-species competition system with feedback controls, Nonlinear Anal. Real World Appl. 9 (2008) 1661-1671. https://doi.org/10.1016/j.nonrwa.2007.05.001
- M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Boston: Birkhauser; 2001.
- Y.K. Li and C. Wang, Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales, Abs. Appl. Anal. 2011 (2011) [Article ID 341520, 22 pp.]
- Y.K. Li, L. Yang and H.T. Zhang, Permanence and uniformly asymptotical stability of almost periodic solutions for a single-species model with feedback control on time scales, Asian-European Journal of Mathematics, in press.
피인용 문헌
- Permanence and Almost Periodic Solution for an Enterprise Cluster Model Based on Ecology Theory with Feedback Controls on Time Scales vol.2013, 2013, https://doi.org/10.1155/2013/639138