Steady-state solutions and stability for a cubic autocatalysis model

Mei-hua Wei; Jianhua Wu; Yinnian He

doi:10.3934/cpaa.2015.14.1147

Article Contents

2015, Volume 14, Issue 3: 1147-1167. Doi: 10.3934/cpaa.2015.14.1147

This issue Previous Article Qualitative analysis of a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses Next Article An elliptic system and the critical hyperbola

Steady-state solutions and stability for a cubic autocatalysis model

1.
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062
2.
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710119
3.
Faculty of Science, Xi’an Jiaotong University, Xi’an 710049

Received: April 30, 2014

Revised: September 30, 2015

Published: April 2015

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Abstract

A reaction-diffusion system, based on the cubic autocatalytic reaction scheme, with the prescribed concentration boundary conditions is considered. The linear stability of the unique spatially homogeneous steady state solution is discussed in detail to reveal a necessary condition for the bifurcation of this solution. The spatially non-uniform stationary structures, especially bifurcating from the double eigenvalue, are studied by the use of Lyapunov-Schmidt technique and singularity theory. Further information about the multiplicity and stability of the bifurcation solutions are obtained. Numerical examples are presented to support our theoretical results.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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