Turing Instability and Hopf Bifurcation for the General Brusselator System

Gai Hui Guo; Bing Fang Li

doi:10.4028/www.scientific.net/AMR.255-260.2126

Paper Titles

A Home Security Monitoring System Study of Intelligent Building
p.2106

Sustainable Development of IT Industry in Taiwan
p.2111

Research on Simulation about a Class of Complex Adaptive System
p.2116

Enhancing the Flexibility of Kademlia under Churn
p.2121

Turing Instability and Hopf Bifurcation for the General Brusselator System
p.2126

Ammonia Detection by Dye Immobilized Microstructured Optical Fiber
p.2131

Application Research of Fuzzy Control for AC Motor on the PLC Platform
p.2136

An Improved P-SVM Model for Patent Application Filings Prediction
p.2141

Super-Resolution Reconstruction of Video Sequences by GST-Driven Adaptive Filtering
p.2145

HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 255-260Turing Instability and Hopf Bifurcation for the...

Turing Instability and Hopf Bifurcation for the General Brusselator System

Abstract:

The Brusselator system subject to homogeneous Neumann boundary conditions is investigated. It is firstly shown that the homogeneous equilibrium solution becomes Turing unstable or diffusively unstable when parameters are chosen properly. Then the existence of Hopf bifurcation to the ODE and PDE models is obtained. Examples of numerical simulations are also shown to support and supplement the analytical results.

You might also be interested in these eBooks

Advances in Civil Engineering, CEBM 2011

View Preview

Info:

Periodical:

Advanced Materials Research (Volumes 255-260)

Pages:

2126-2130

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.255-260.2126

Citation:

Cite this paper

Online since:

May 2011

Authors:

Gai Hui Guo, Bing Fang Li

Keywords:

Brusselator System, Diffusion, Hopf Bifurcation, Stability

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] I. Prigogene, R. Lefever, Symmetry breaking instabilities in dissipative systems II, J. Chem. Phys. 48 (1968) 1665-1700.

Google Scholar

[2] K. Brown, F.A. Davidson, Global bifurcation in the Brusselator system, Nonlinear Anal. TMA 12 (1995) 1713-1725.

DOI: 10.1016/0362-546x(94)00218-7

Google Scholar

[3] R. Peng, M. Wang, Pattern formation in the Brusselator system, J. Math. Anal. Appl. 309 (2005) 151-166.

Google Scholar

[4] Y. You, Global dynamics of the Brusselator equations, Dyn. Partial Diff. Eqns. 4 (2007) 167-196.

Google Scholar

[5] B. Li, M. Wang, Diffusive driven instability and Hopf bifurcation in the Brusselator system, Appl. Math. Mech., 29 (2008) 825-832.

DOI: 10.1007/s10483-008-0614-y

Google Scholar

[6] M. Ghergu, Non-constant steady-state solutions for Brusselator type systems, Nonlinearity 21 (2008) 2331-2345.

DOI: 10.1088/0951-7715/21/10/007

Google Scholar

[7] R. Peng, M. Wang, On steady-state solutions of the Brusselator-type system, Nonlinear Anal. TMA 71 (2009) 1389-1394.

Google Scholar

[8] F. Yi, J.Wei, J. Shi, Diffusion-driven instability and bifurcation in the Lengyel-Epstein system, Nonlinear Anal. 9 (2008) 1038-1051.

DOI: 10.1016/j.nonrwa.2007.02.005

Google Scholar

[9] F. Yi, J. Wei, J. Shi, Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system, J. Differential Equations 246 (2009) 1944-1977.

DOI: 10.1016/j.jde.2008.10.024

Google Scholar

[10] Q. Lu, Qualitative Method and Bifurcation of Ordinary Differential Equations, Beijing Aviation and Spaceflight University Press, Beijing, 1989.

Google Scholar