Sublinear discrete-time order-preserving dynamical systems

Mathematical Proceedings of the Cambridge Philosophical Society

Volumn 119, Issue 3, 1996, Pages 561-574

  Jiang, J F ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

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EID: 21844518538     PISSN: 03050041     EISSN: 14698064     Source Type: Journal    
DOI: 10.1017/S0305004100074417     Document Type: Article

References (24)

1. M.W. HlBSCH. Systems of differential equations that are competitive or cooperative. II: Convergence almost everywhere. SIAM J. Math. Anal. 16 (1985), 432–439.
2. M. W. Hibsch. Systems of differential equations that are competitive or cooperative. V: Convergence in 3-dimensional systems. J. Diff. Eqns. 80 (1989), 94–106.
3. M. W. Hirsch. Stability and convergence in strongly monotone dynamical systems. J. reine angew. Math. 383 (1988), 1–53.
4. M. W. Hiksch. The dynamical systems approach to differential equations. Bull. Amer. Math. Soc. 11 (1984), 1–64.
5. H. Matano. Strong comparison principle in nonlinear parabolic equations: in Nonlinear parabolic equations: qualitative properties of solutions (L. Boccardo and A. Tesei, eds.), Pitman Res. Notes in Math. 149 (Longman Scientific and Technical, 1987), 148–155.
6. H. L. Smith and H. R. Thieme. Quasiconvergence and stability for strongly order-preserving semiflows. SIAM J. Math. Anal. 21 (1990), 673–692.
7. H. L. Smith and H. R. Thieme. Convergence for strongly order-preserving semiflows. SIAM J.Math. Anal. 22 (1991), 1081–1101.
8. H. L. Smith. Cooperative systems of differential equations with concave nonlinearities. J. Nonlinear Anal. 10 (1986), 1037–1052.
9. P. Polacik. Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. J. Diff. Eqns. 79 (1989), 89–110.
10. N. D. Alikakos and P. Hess. On stabilization of discrete monotone dynamical systems. Israel J.Math. 59 (1987), 185–194.
11. X. D. Alikakos, P. Hess and H. Matano. Discrete order preserving semigroups and stability for periodic parabolic differential equations. J. Diff. Eqns. 82 (1989), 322–341.
12. P. Takác. Convergence to equilibrium on invariant d-hypersurfaces for strongly increasing discrete-time semigroups. J. Math. Anal. Appl. 148 (1990), 223–244.
13. P. Takác. Asymptotic behavior of discrete-time semigroups of sublinear, strongly increasing mappings with applications to biology. J. Nonlinear Anal. 14 (1990), 35–42.
14. E. X. Dancer and P. Hess. Stability of fixed points for order-preserving discrete-time dynamical systems. J. reine angew. Math. 419 (1991), 125–139.
15. J. F. Jiang. Convergence to trap almost everywhere for flows generated by cooperative and irreducible vector fields. Chin. Ann. of Math. Series B 14 (1993), 165–174.
16. J. F. Jiang. A Liapunov function for three-dimensional feedback systems. Proc. Amer. Math. Soc. 114 (1992), 1009–1013.
17. J. F. Jiang. A Liapunov function for 4-dimensional positive feedback systems. Quarterly Appi. Math. LII (1994), 601–614.
18. J. F. Jiang. The algebraic criteria for the asymptotic behavior of cooperative systems with concave nonlinearities. J. Systems Sci. Math. Sci. 6 (1993), 193–208.
19. J. F. Jiang. A note on a global stability theorem of M. W. Hirsch. Proc. Amer. Math. Soc. 112 (1991), 803–806.
20. J. F. Jiang. On the global stability of cooperative systems. Bull. LondonMath. Soc. 26 (1994), 455–458.
21. J. F. Jiang. Three- and four-dimensional cooperative systems with every equilibrium stable. J. Math. Anal. Appl. 188 (1994), 92–100.
22. J. F. Jiang. On the analytic order-preserving discrete-time dynamical systems in Rʼn with every fixed point stable. To appear in J. London Math. Soc.
23. W. A. Coppel. Stability and asymptotic behavior of differential equations (Heath, 1965).
24. H. L. Smith. Periodic solutions of periodic competitive and cooperative systems. SIAM J. Math. Anal. 17 (1986), 1289–1318.