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On the global attractivity of monotone random dynamical systems

Authors: Feng Cao and Jifa Jiang
Journal: Proc. Amer. Math. Soc. 138 (2010), 891-898
MSC (2000): Primary 37H05, 37C65, 34D05
Published electronically: November 3, 2009
MathSciNet review: 2566555
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Abstract: Suppose that $ (\theta,\varphi)$ is a monotone (order-preserving) random dynamical system (RDS for short) with state space $ V$, where $ V$ is a real separable Banach space with a normal solid minihedral cone $ V_{+}$. It is proved that the unique equilibrium of $ (\theta,\varphi)$ is globally attractive if every pull-back trajectory has compact closure in $ V$.

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Additional Information

Feng Cao
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China

Jifa Jiang
Affiliation: School of Science and Mathematics, Shanghai Normal University, Shanghai 200234, People’s Republic of China

Keywords: Random dynamical systems, monotonicity, global stability
Received by editor(s): September 23, 2008
Received by editor(s) in revised form: January 17, 2009
Published electronically: November 3, 2009
Additional Notes: The second author is partially supported by Chinese NNSF grants 10671143 and 10531030 and Shanghai NSF grant 09ZR1423100 and is the corresponding author.
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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