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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
Affiliation:
School of Mathematics and Statistics, Southwest University, Chongqing 400715, People's Republic of China, (jzhouwm@gmail.com)
Junping Shi
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA, (jxshix@wm.edu)

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
Copyright
Copyright © Royal Society of Edinburgh 2014 

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