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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 119, Issue 3
  • April 1996, pp. 561-574

Sublinear discrete-time order-preserving dynamical systems

  • J. F. Jiang (a1)
  • DOI:
  • Published online: 24 October 2008

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.

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[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.

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[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.

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