Uniform persistence in processes with application to nonautonomous competitive models

Journal of Mathematical Analysis and Applications

Volumn 258, Issue 1, 2001, Pages 87-101

  Zhao, Xiao Qiang ^a  

^a MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Continuous processes; skew product semiflows; uniform persistence; competitive models

Indexed keywords

EID: 0013126266     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7361     Document Type: Article

References (25)

1. Ahmad S. Extinction of species in nonautonomous Lotka-Volterra systems. Proc. Amer. Math. Soc. 127:1999;2905-2910.
2. Burton T. A., Hutson V. Permanence for non-autonomous predator-prey systems. Diff. Integ. Equa. 4:1991;1269-1280.
3. Butler G. J., Waltman P. Persistence in dynamical systems. J. Diff. Equa. 63:1986;255-263.
4. Dafermos C. Semiflows generated by compact and uniform processes. Math. Syst. Theory. 8:1975;142-149.
5. Fernandes M. L. C. Uniform repellers for processes with applications to periodic differential systems. J. Diff. Equa. 86:1990;141-157.
6. Hale J. K. Asymptotic Behavior of Dissipative Systems. Mathematical Surveys and Monographs. 25:1988;American Mathematical Society, Providence.
7. Hale J. K., Waltman P. Persistence in infinite-dimensional systems. SIAM J. Math. Anal. 20:1989;388-395.
8. Hirsch M. W., Smith H. L., Zhao X.-Q. Chain transitivity, attractivity and strong repellors for semidynamical systems. J. Dynam. Diff. Equa. 13:2001;107-131.
9. Hutson V., Schmitt K. Permanence and the dynamics of biological systems. Math. Biosci. 111:1992;1-71.
10. LaSalle J. P. The Stability of Dynamical Systems. 1976;Society for Industrial and Applied Mathematics, Philadelphia.
11. Mischaikow K., Smith H. L., Thieme H. R. Asymptotically autonomous semi-flows: chain recurrence and Liapunov functions. Trans. Amer. Math. Soc. 347:1995;1669-1685.
12. Montes de Oca F., Zeeman M. L. Extinction in nonautonomous competitive Lotka-Volterra systems. Proc. Amer. Math. Soc. 124:1996;3677-3687.
13. Sell G. Topological Dynamics and Ordinary Differential Equations. 1971;Van Nostrand Reinhold, London.
14. Smith H. L., Waltman P. The Theory of the Chemostat. 1995;Cambridge University Press, Cambridge.
15. Smith H. L., Zhao X.-Q. Dynamics of a periodically pulsed bio-reactor model. J. Diff. Equa. 155:1999;368-404.
16. Thieme H. R. Convergence results and Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations. J. Math. Biol. 30:1992;755-763.
17. Thieme H. R. Persistence under relaxed point-dissipativity (with application to an epidemic model). SIAM J. Math. Anal. 24:1993;407-435.
18. Thieme H. R. Uniform weak implies uniform strong persistence for non-autonomous semiflows. Proc. Amer. Math. Soc. 127:1999;2395-2403.
19. Thieme H. R. Uniform persistence and permanence for non-autonomous semiflows in population biology. Math. Biosci. 166:2000;173-201.
20. Waltman P. A brief survey of persistence in dynamical systems. Delay-differential Equations and Dynamical Systems. Lecture Notes in Mathematics. 1475:1991;Springer, New York.
21. Wolkowicz G. S. K., Zhao X.-Q. N-species competition in a periodic chemostat. Diff. Integral Equa. 11:1998;465-491.
22. Wu J., Zhao X.-Q., He X. Global asymptotic behavior in almost periodic Kolmogorov equations and chemostat models. Nonlinear World. 3:1996;589-611.
23. Zhao X.-Q. Uniform persistence and periodic coexistence states in infinite-dimensional periodic semiflows with applications. Canadian Appl. Math. Quart. 3:1995;473-495.
24. Zhao X.-Q. Asymptotic behavior for asymptotically periodic semiflows with applications. Comm. on Applied Nonlinear Anal. 3:1996;43-66.
25. Zhao X.-Q. Convergence in asymptotically periodic tridiagonal competitive-cooperative systems. Canadian Appl. Math. Quart. 6:1998;287-301.