Lemmens, Bas and Akian, Marianne and Gaubert, Stephane (2011) Stability and convergence in discrete convex monotone dynamical systems. Journal of Fixed Point Theory and Applications, 9 (2). pp. 295-325. ISSN 1661-7738. (doi:https://doi.org/10.1007/s11784-011-0052-1) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)
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We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on n letters, where n is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus|
|Depositing User:||Bas Lemmens|
|Date Deposited:||18 Nov 2011 14:32 UTC|
|Last Modified:||04 Oct 2012 09:55 UTC|
|Resource URI:||https://kar.kent.ac.uk/id/eprint/28445 (The current URI for this page, for reference purposes)|