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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A sufficient condition for bifurcation in random dynamical systems


Authors: Xiaopeng Chen, Jinqiao Duan and Xinchu Fu
Journal: Proc. Amer. Math. Soc. 138 (2010), 965-973
MSC (2000): Primary 37H20, 37B30, 60H10
Published electronically: October 19, 2009
MathSciNet review: 2566563
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Abstract: Some properties of the random Conley index are obtained, and then a sufficient condition for the existence of abstract bifurcation points for both discrete-time and continuous-time random dynamical systems is presented. This stochastic bifurcation phenomenon is demonstrated by a few examples.


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Additional Information

Xiaopeng Chen
Affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
Email: chenxiao002214336@yahoo.cn

Jinqiao Duan
Affiliation: Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616
Email: duan@iit.edu

Xinchu Fu
Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
Email: xcfu@shu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10093-X
PII: S 0002-9939(09)10093-X
Keywords: Random dynamical systems, discrete-time and continuous-time dynamical systems, random homeomorphism, Conley index, abstract bifurcation point
Received by editor(s): April 19, 2009
Received by editor(s) in revised form: June 24, 2009
Published electronically: October 19, 2009
Additional Notes: The first author would like to thank Zhenxin Liu for helpful comments.
The second author was supported in part by NSF Grant 0620539, the Cheung Kong Scholars Program and the K. C. Wong Education Foundation.
The third author was supported in part by NSFC Grant 10672146.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.