Skip to main content
    • Aa
    • Aa

Sublinear discrete-time order-preserving dynamical systems

  • J. F. Jiang (a1)

Suppose that the continuous mapping is order-preserving and sublinear. If every positive semi-orbit has compact closure, then every positive semi-orbit converges to a fixed point. This result does not require that the order be strongly preserved.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] M. W. Hirsch . Systems of differential equations that are competitive or cooperative. II: Convergence almost everywhere. SIAM J. Math. Anal. 16 (1985), 432439.

[2] M. W. Hirsch . Systems of differential equations that are competitive or cooperative. V: Convergence in 3-dimensional systems. J. Diff. Eqns. 80 (1989), 94106.

[4] M. W. Hirsch . The dynamical systems approach to differential equations. Bull. Amer. Math. Soc. 11 (1984), 164.

[6] H. L. Smith and H. R. Thieme . Quasiconvergence and stability for strongly order-preserving semiflows. SIAM J. Math. Anal. 21 (1990), 673692.

[7] H. L. Smith and H. R. Thieme . Convergence for strongly order-preserving semiflows. SIAM J.Math. Anal. 22 (1991), 10811101.

[8] H. L. Smith . Cooperative systems of differential equations with concave nonlinearities. J. Nonlinear Anal. 10 (1986), 10371052.

[9] P. Polaĉik . Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. J. Diff. Eqns. 79 (1989), 89110.

[10] N. D. Alikakos and P. Hess . On stabilization of discrete monotone dynamical systems. Israel J.Math. 59 (1987), 185194.

[11] N. D. Alikakos , P. Hess and H. Matano . Discrete order preserving semigroups and stability for periodic parabolic differential equations. J. Diff. Eqns. 82 (1989), 322341.

[12] P. Takáĉ . Convergence to equilibrium on invariant d-hypersurfaces for strongly increasing discrete-time semigroups. J. Math. Anal. Appl. 148 (1990), 223244.

[13] P. Takáĉc . Asymptotic behavior of discrete-time semigroups of sublinear, strongly increasing mappings with applications to biology. J. Nonlinear Anal. 14 (1990). 3542.

[16] J. F. Jiang . A Liapunov function for three-dimensional feedback systems. Proc. Amer. Math. Soc. 114 (1992), 10091013.

[19] J. F. Jiang . A note on a global stability theorem of M. W. Hirsch. Proc. Amer.Math. Soc. 112 (1991), 803806.

[21] J. F. Jiang . Three- and four-dimensional cooperative systems with every equilibrium stable. J. Math. Anal. Appl. 188 (1994), 92100.

[24] H. L. Smith . Periodic solutions of periodic competitive and cooperative systems. SIAM J. Math. Anal. 17 (1986), 12891318.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 1 *
Loading metrics...

Abstract views

Total abstract views: 17 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 28th May 2017. This data will be updated every 24 hours.