Stability and convergence in discrete convex monotone dynamical systems
Stability and convergence in discrete convex monotone dynamical systems
复制标题
离散凸单调动力系统的稳定性和收敛性
DOI：
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发表时间：
2010
期刊：
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通讯作者：
Bas Lemmens
中科院分区：
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作者：
M. Akian;S. Gaubert;Bas Lemmens
研究了映射为凸单调的离散动力系统相对于标准正锥的稳定行为。引入了不动点和周期点的切向稳定性的概念，它比Lyapunov稳定性弱。其中证明了切向稳定不动点的集合同构于凸半格，并给出了唯一切向稳定不动点存在的判据。我们还证明了切向稳定周期点的周期是n个字母上的排列顺序，其中n是基础空间的维数，并给出了全局收敛到周期轨道的充分条件。
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.