Permanence in nonautonomous multi-species predator-prey system with feedback controls

Applied Mathematics and Computation

Volumn 173, Issue 2, 2006, Pages 694-709

  Chen, Fengde ^a  

^a FUZHOU UNIVERSITY   (China)

Author keywords

Feedback control; Globally asymptotic stability; Lower average; Lyapunov function; Permanence; Predator prey; Upper average

Indexed keywords

LYAPUNOV METHODS; TOXIC MATERIALS;

PERMANENCE; PREDATOR-PREY; UPPER AVERAGE;

FEEDBACK CONTROL;

EID: 32644443693     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.04.047     Document Type: Article

References (30)

1. K. Gopalsamy Global asymptotic stability in a periodic Lotka-Volterra system J. Austral. Math. Soc. Ser. B 27 1985 66 72
2. X.Q. Zhao The qualitative analysis of n-species Lotka-Volterra periodic competition systems Math. Comput. Model. 15 11 1991 3 8
3. A. Tineo, and C. Alvarz A different consideration about the globally asymptotically stable solution of the periodic n-competing species problem J. Math. Anal. Appl. 159 1991 44 55
4. C.Y. He On almost periodic solutions of Lotka-Volterra almost periodic competition systems Ann. Diff. Eqs. 9 1 1993 26 36
5. K. Gopalsamy Global asymptotic stability in a almost periodic Lotka-Volterra system J. Austral. Math. Soc. Ser. B 27 1986 346 360
6. J. Cui, and L. Chen Asymptotic behavior of the solution for a class of time-dependent competitive system with feedback controls Ann. Diff. Eqs. 9 1 1993 11 17
7. J. Chattopadhyay Effect of toxic substance on a two-species competitive system Ecol. Model 84 1996 287 289
8. J. Maynard-Smith Models in Ecology 1974 Cambridge University Cambridge
9. X.Y. Song, and L.S. Chen Periodic solutions of a delay differential equation of plankton allelopathy Acta Math. Sci. 23 A 2003 8 13 (in Chinese)
10. Z. Jin, and Z.E. Ma Periodic solutions for delay differential equations model of plankton allelopathy Comput. Math. Appl. 44 2002 491 500
11. P. Yang, and R. Xu Global attractivity of the periodic Lotka-Volterra system J. Math. Anal. Appl. 233 1 1999 221 232
12. J.D. Zhao, and W.C. Chen Global asymptotic stability of a periodic ecological model Appl. Math. Comput. 147 3 2004 881 892
13. Y. Xia Existence and global attractivity of an almost periodic ecological model Appl. Math. Comput. 157 2 2004 449 475
14. J.D. Zhao, and J.F. Jiang Permanence in nonautonomous Lotka-Volterra system with predator-prey Appl. Math. Comput. 152 2004 99 109
15. P.X. Weng Global attractivity in a periodic competition system with feedback controls Acta Appl. Math. 12 1996 11 21
16. P.X. Weng Existence and global stability of positive periodic solution of periodic integro-differential systems with feedback controls Comput. Math. Appl. 40 2000 747 759
17. P.X. Weng, and D.Q. Jiang Existence and global stability of positive periodic solution of n-species periodic Lotka-Volterra competition systems with feedback controls and deviating arguments Far East J. Math. Sci. 7 1 2002 45 65
18. Y.N. Xiao, S.Y. Tang, and J.F. Chen Permanence and periodic solution in competition system with feedback controls Math. Comput. Model. 27 6 1998 33 37
19. K. Gopalsamy, and P.X. Weng Feedback regulation of logistic growth Int. J. Math. Sci. 16 1 1993 177 192
20. F. Yang, and D.Q. Jiang Existence and global attractivity of positive periodic solution of a logistic growth system with feedback control and deviating arguments Ann. Diff. Eqs. 17 4 2001 337 384
21. X.Y. Li, M. Fan, and K. Wang Positive periodic solution of single species model with feedback regulation and infinite delay Appl. Math. J. Chin. Univ. Ser. A 17 1 2002 13 21 (in Chinese)
22. M. Fan, 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 Math. Sin. 19 4 2003 801 822
23. H. Huo, and W. Li Positive periodic solutions of a class of delay differential system with feedback control Appl. Math. Comput. 148 1 2004 35 46
24. F.Q. Yin, and 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
25. F.D. Chen, F.X. Lin, and X.X. Chen Sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control Appl. Math. Comput. 158 1 2004 45 68
26. F.D. Chen, Positive periodic solutions of neutral Lotka-Volterra system with feedback control, Appl. Math. Comput., in press.
27. Y.H. Xia, J.D. Cao, H.Y. Zhang, and F.D. Chen Almost periodic solutions in n-species competitive system with feedback controls J. Math. Anal. Appl. 294 2004 504 522
28. Z.K. Huang, and F.D. Chen Almost periodic solution of two species model with feedback regulation and infinite delay J. Eng. Math. 20 5 2004 33 40
29. S. Ahmad, and A.C. Lazer Average conditions for global asymptotic stability in a nonautonomous Lotka-Volterra system Nonlin. Anal. 40 2000 37 49
30. J.D. Zhao, J.F. Jiang, and A.C. Lazer The permanence and global attractivity in a nonautonomous Lotka-Volterra system Nonlin. Anal.: Real World Appl. 5 4 2004 265 276