Journal of Mathematical Chemistry

, Volume 51, Issue 8, pp 2001–2019 | Cite as

Bifurcation analysis of reaction–diffusion Schnakenberg model

Original Paper


Bifurcations of spatially nonhomogeneous periodic orbits and steady state solutions are rigorously proved for a reaction–diffusion system modeling Schnakenberg chemical reaction. The existence of these patterned solutions shows the richness of the spatiotemporal dynamics such as oscillatory behavior and spatial patterns.


Schnakenberg model Steady state solution Hopf bifurcation  Steady state bifurcation Pattern formation 

Mathematics Subject Classification (2000)

58F07 58C28 58C15 34C23 35B20 35B32 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Ping Liu
    • 1
  • Junping Shi
    • 2
  • Yuwen Wang
    • 1
  • Xiuhong Feng
    • 1
  1. 1.Y.Y. Tseng Functional Analysis Research Center and School of Mathematical SciencesHarbin Normal UniversityHarbinPeople’s Republic of China
  2. 2.Department of MathematicsCollege of William and MaryWilliamsburgUSA

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