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# Generic Quasi-Convergence for Essentially Strongly Order-Preserving Semiflows

Published:2009-06-01
Printed: Jun 2009
• Taishan Yi
• Xingfu Zou
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## Abstract

By employing the limit set dichotomy for essentially strongly order-preserving semiflows and the assumption that limit sets have infima and suprema in the state space, we prove a generic quasi-convergence principle implying the existence of an open and dense set of stable quasi-convergent points. We also apply this generic quasi-convergence principle to a model for biochemical feedback in protein synthesis and obtain some results about the model which are of theoretical and realistic significance.
 Keywords: Essentially strongly order-preserving semiflow, compactness, quasi-convergence
 MSC Classifications: 34C12 - Monotone systems 34K25 - Asymptotic theory

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