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Qualitative analysis of an autocatalytic chemical reaction model with decay

Published online by Cambridge University Press:  20 March 2014

Jun Zhou  and
Junping Shi
Jun Zhou
Affiliation:
School of Mathematics and Statistics, Southwest University, Chongqing 400715, People's Republic of China, ([email protected])
Junping Shi
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA, ([email protected])
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Abstract

In this paper, we revisit a reaction—diffusion autocatalytic chemical reaction model with decay. For higher-order reactions, we prove that the system possesses at least two positive steady-state solutions; hence, it has bistable dynamics similar to the system without decay. For the linear reaction, we determine the necessary and sufficient condition to ensure the existence of a solution. Moreover, in the one-dimensional case, we prove that the positive steady-state solution is unique. Our results demonstrate the drastic difference in dynamics caused by the order of chemical reactions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 2 , April 2014 , pp. 427 - 446
Copyright
Copyright © Royal Society of Edinburgh 2014 

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