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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Phase-translation group actions on strongly monotone skew-product semiflows


Authors: Qiang Liu and Yi Wang
Journal: Trans. Amer. Math. Soc. 364 (2012), 3781-3804
MSC (2010): Primary 37B55, 37C65, 37L15, 37N25
Published electronically: February 27, 2012
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Abstract: We establish a convergence property for pseudo-bounded forward orbits of strongly monotone skew-product semiflows with invariant phase-translation group actions. The results are then applied to obtain global convergence of certain chemical reaction networks whose associated systems in reaction coordinates are monotone, as well as the dynamics of certain reaction-diffusion systems in time-recurrent structure including periodicity, almost periodicity and almost automorphy.


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Additional Information

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

Yi Wang
Affiliation: Wu Wen-Tsun Key Laboratory of Mathematics, Department of Mathematics, University of Science and Technology of China Hefei, Anhui, 230026, People’s Republic of China – and – Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FIN-00014, Finland

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05555-3
PII: S 0002-9947(2012)05555-3
Received by editor(s): September 10, 2009
Received by editor(s) in revised form: January 22, 2011
Published electronically: February 27, 2012
Additional Notes: The second author was the corresponding author and was partially supported by NSF of China No. 10971208 and by the Finnish Center of Excellence in Analysis and Dynamics and the FRF for the Central Universities
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.