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On the Global Stability of Cooperative Systems
Author(s) -
JiFa Jiang
Publication year - 1994
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/26.5.455
Subject(s) - mathematics , closure (psychology) , orbit (dynamics) , stability (learning theory) , vector field , pure mathematics , stability theory , field (mathematics) , geometry , physics , quantum mechanics , aerospace engineering , computer science , law , political science , nonlinear system , machine learning , engineering
Suppose that F is a C 1 cooperative vector field on X , where X = R n or Intℝ + n , or [[ p, q ]]. We prove that the unique equilibrium of F is globally asymptotically stable if and only if every forward semi‐orbit has compact closure in X .
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