Almost Periodic Sequence Solutions of a Discrete Cooperation System with Feedback Controls
In this paper, we consider the almost periodic solutions of a discrete cooperation system with feedback controls. Assuming that the coefficients in the system are almost periodic sequences, we obtain the existence and uniqueness of the almost periodic solution which is uniformly asymptotically stable.
[1] J.A. Cui, L.S. Chen, Global asymptotic stability in a nonautonomous
cooperative system, Syst. Sci. Math. Sci. 6 (1993) 44-51.
[2] R.P. Agarwal, Difference Equations and Inequalities: Theory, Methods
and Applications, vol. 228 of Monographs and Textbooks in Pure and
Applied Mathematics, Marcel Dekker, New York, NY, USA, 2000.
[3] J.D. Murray, Mathematical Biology, vol. 19 of Biomathematics, Springer,
Berlin, Germany, 1989.
[4] L. Bai, M. Fan, K. Wang, Existence of positive solution for difference
equation of the cooperative system, J. Biomath. 19 (2004) 271-279 (in
Chinese).
[5] X. Chen, C. Fengde, Stable periodic solution of a discrete periodic
Lotka-Volterra competition system with a feedback control, Appl. Math.
Comput. 181 (2006) 1446-1454.
[6] F.Q. Yin, Y.K. Li, Positive periodic solutions of a single species model
with feedback regulation and distributed time delay, Appl. Math. Comput.
153 (2004) 475-484.
[7] L.F. Nie, J.G. Peng, Z.D. Teng, Permanence and stability in multispecies
nonautonomous Lotka-Volterra competitive systems with delays
and feedback controls, Math. Comput. Modelling 49 (2009) 295-306.
[8] Z. Wang and Y.K. Li, Almost periodic solutions of a discrete mutualism
model with Feedback controls, Discrete Dynamics in Nature and Society
2010 (2010), Article ID 286031, pp. 18.
[9] D. Cheban, C. Mammana, Invariant, manifolds, global attractors and
almost periodic Solutions of nonautonomous difference equations, Nonlinear
Anal. 56 (2004) 465-484.
[10] L.J. Chen, L.J. Chen, Z. Li, Permanence of a delayed discrete mutualism
model with feedback controls Mathe. Comput. Modelling 50 (2009) 1083-
1089.
[11] S. N. Zhang, Existence of almost periodic solution for difference
systems, Ann. Diff. Equs. 16 (2000) 184-206.
[1] J.A. Cui, L.S. Chen, Global asymptotic stability in a nonautonomous
cooperative system, Syst. Sci. Math. Sci. 6 (1993) 44-51.
[2] R.P. Agarwal, Difference Equations and Inequalities: Theory, Methods
and Applications, vol. 228 of Monographs and Textbooks in Pure and
Applied Mathematics, Marcel Dekker, New York, NY, USA, 2000.
[3] J.D. Murray, Mathematical Biology, vol. 19 of Biomathematics, Springer,
Berlin, Germany, 1989.
[4] L. Bai, M. Fan, K. Wang, Existence of positive solution for difference
equation of the cooperative system, J. Biomath. 19 (2004) 271-279 (in
Chinese).
[5] X. Chen, C. Fengde, Stable periodic solution of a discrete periodic
Lotka-Volterra competition system with a feedback control, Appl. Math.
Comput. 181 (2006) 1446-1454.
[6] F.Q. Yin, Y.K. Li, Positive periodic solutions of a single species model
with feedback regulation and distributed time delay, Appl. Math. Comput.
153 (2004) 475-484.
[7] L.F. Nie, J.G. Peng, Z.D. Teng, Permanence and stability in multispecies
nonautonomous Lotka-Volterra competitive systems with delays
and feedback controls, Math. Comput. Modelling 49 (2009) 295-306.
[8] Z. Wang and Y.K. Li, Almost periodic solutions of a discrete mutualism
model with Feedback controls, Discrete Dynamics in Nature and Society
2010 (2010), Article ID 286031, pp. 18.
[9] D. Cheban, C. Mammana, Invariant, manifolds, global attractors and
almost periodic Solutions of nonautonomous difference equations, Nonlinear
Anal. 56 (2004) 465-484.
[10] L.J. Chen, L.J. Chen, Z. Li, Permanence of a delayed discrete mutualism
model with feedback controls Mathe. Comput. Modelling 50 (2009) 1083-
1089.
[11] S. N. Zhang, Existence of almost periodic solution for difference
systems, Ann. Diff. Equs. 16 (2000) 184-206.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56417", author = "Ziping Li and Yongkun Li", title = "Almost Periodic Sequence Solutions of a Discrete Cooperation System with Feedback Controls", abstract = "In this paper, we consider the almost periodic solutions of a discrete cooperation system with feedback controls. Assuming that the coefficients in the system are almost periodic sequences, we obtain the existence and uniqueness of the almost periodic solution which is uniformly asymptotically stable.
", keywords = "Discrete cooperation model, almost periodic solution, feedback control, Lyapunov function.", volume = "5", number = "8", pages = "1284-9", }
