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On the Analytic Order‐Preserving Discrete‐Time Dynamical Systems in ℝ n with every Fixed Point Stable
Author(s) -
JiFa Jiang
Publication year - 1996
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/53.2.317
Subject(s) - fixed point , mathematics , dynamical systems theory , orbit (dynamics) , closure (psychology) , conjecture , order (exchange) , dynamical system (definition) , discrete time and continuous time , fixed point theorem , pure mathematics , mathematical analysis , control theory (sociology) , computer science , physics , control (management) , statistics , finance , quantum mechanics , economics , artificial intelligence , engineering , market economy , aerospace engineering
This paper studies the asymptotic behaviour of an analytic order‐preserving discrete‐time dynamical system in ℝ n , which is usually generated by a periodic cooperative system. The author proves that for such a dynamical system, if every fixed point is Liapunov stable and every positive semi‐orbit has compact closure, then every positive semi‐orbit converges. This result does not require the assumption ‘strongly’ and gives an affirmative answer to the conjecture proposed by the author in [ 17 ] for the analytic case.