Global attractivity and stability in some monotone discrete dynamical systems

Bulletin of the Australian Mathematical Society

Volumn 53, Issue 2, 1996, Pages 305-324

  Zhao, Xiao Qiang ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000224082     PISSN: 00049727     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0004972700017032     Document Type: Article

References (28)

1. H. Amann, 'Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces', SIAM Rev. 18 (1976), 620-709.
2. G. Aronsson and R.B. Kellogg, 'On a differential equation arising from compartmental analysis', Math. Biosci. 38 (1973), 113-122.
3. R.S. Cantrell and C. Cosner, 'Diffusive logistic equations with indefinite weights: population models in disrupted envionments', Proc. Roy. Soc. Edinburgh Sect. A 112 (1989), 293-318.
4. R.S. Cantrell and C. Cosner, 'Diffusive logistic equations with indefinite weights: population models in disrupted envionments II', SIAM J. Math. Anal. 22 (1991), 1043-1064.
5. E.N. Dancer, 'Fixed point index calculations and applications', in Topological nonlinear analysis, degree, singularity and variation, (M. Matzeu and A. Vignili, Editors) (Birkhauser, 1995).
6. E.N. Dancer and P. Hess, 'On stable solutions of quasilinear periodic-parabolic problems', Ann. Scuola Norm. Sup. Pisa Cl. Sci. 14 (1987), 123-141.
7. E.N. Dancer and P. Hess, 'Stability of fixed points for order-preserving discrete-time dynamical systems', J. Reine Angew. Math. 419 (1991), 125-139.
8. D. Daners, 'Qualitative behavior of an epidemics model', Differential Integral Equations 5 (1992), 1017-1032.
9. J.K. Hale, Asymptotic behavior of dissipative systems, Math. Surveys Monographs 25 (Amer. Math. Soc., Providence, RI, 1988).
10. J.K. Hale and G. Rangel, 'Convergence in gradient-like systems with applications to PDE', Z. Angew. Math. Phys. 43 (1992), 63-124.
11. J.K. Hale and P. Waltman, 'Persistence in infinite dimensional systems', SIAM J. Math. Anal. 20 (1989), 388-395.
12. D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Math. 840 (Springer-Verlag, Berlin, 1981).
13. P. Hess, Periodic-parabolic boundary value problems andpositivity, Pitman Research Notes in Math. 247 (Longman Scientific and Technical, 1991).
14. M.W. Hirsch, 'The dynamical systems approach to differential equations', Bull. Amer. Math. Soc. 11 (1984), 1-64.
15. M. W. Hirsch, 'Systems of differential equations that are competitive or cooperative II: convergence almost everywhere', SIAM J. Math. Anal. 16 (1985), 423-439.
16. M.W. Hirsch, 'Stability and convergence in strongly monotone dynamical systems', J. Reine Angew. Math. 383 (1988), 1-53.
17. S.-B. Hsu and P. Waltman, 'On a system of reaction-diffusion equations arising from competition in an unstirred Chemostat', SIAM J. Appl. Math. 53 (1993), 1026-1044.
18. M.A. Krasnoselskii, Translation along trajectories of differential equations, Translations of Math. Monographs 19 (Amer. Math. Soc., Providence, R.I., 1968).
19. H. Matano, 'Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems', J. Fac. Sci. Univ. Tokyo Sect. IA Math. 30 (1984), 645-673.
20. P. Poláčik, 'Convergence in smooth strongly monotone flows defined by semilinear parabolic equations', J. Differential Equations 79 (1989), 89-110.
21. P. Poláčik and I. Tereščák, 'Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems', Arch. Rational Mech. Anal. 116 (1991), 339-360.
22. H. L. Smith, 'Cooperative systems of differential equations with concave nonlinearities', Nonlinear Anal. 10 (1986), 1037-1052.
23. H.L. Smith and H.R. Thieme, 'Convergence for strongly order-preserving semiflows', SIAM J. Math. Anal. 22 (1991), 1081-1101.
24. J. So and P. Waltman, 'A nonlinear boundary value problem arising from competition in the Chmostat', Appl. Math. Comput. 32 (1989), 169-183.
25. P. Takáč, 'Asymptotic behavior of discrete-time semigroups of sublinear, strongly increasing mappings with applications in biology', Nonlinear Anal. 14 (1990), 35-42.
26. E. Zeidler, Nonlinear functional analysis and its applications I. Fixed-point theory (Berlin, Heidelberg, New York, 1986).
27. X.-Q. Zhao and V. Hutson, 'Permanence in Kolmogorov periodic predator-prey models with diffusion', Nonlinear Anal. 23 (1994), 651-668.
28. X.-Q. Zhao and B.D. Sleeman, 'Permenence in Kolmogorov competition models with diffusion', IMA J. Applied Math. 51 (1993), 1-11.