Analysis on bifurcation and stability of a generalized Gray–Scott chemical reaction model

Jingjing Wang and Yunfeng Jia

Physica A: Statistical Mechanics and its Applications, 2019, vol. 528, issue C

Abstract: In numerous chemical reactions, the autocatalytic reaction is a very important and characteristic catalytic reaction. The Gray–Scott model is an extremely representative autocatalytic reaction model among many catalytic chemical reaction models. This paper deals with a generalized Gray–Scott chemical reaction model. Firstly, we give the a priori estimates of positive solutions. Secondly, we discuss the conditions which ensure the model permitting a local bifurcating solution. Thirdly, we investigate the stable property of the bifurcating solution by using a new idea. Finally, the numerical simulations are carried out to illustrate the rich dynamical behaviors of the model including the existence and stability of bifurcating solution. The result shows that the system exhibits abundant dynamical behaviors and the chemical reaction in reactor will be in balance in the end under certain conditions.

Keywords: Generalized Gray–Scott model; Bifurcation; Stability; Numerical simulations (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:528:y:2019:i:c:s0378437119308143

DOI: 10.1016/j.physa.2019.121394

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