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Applied Mathematics and Mechanics

, Volume 28, Issue 9, pp 1235–1248 | Cite as

Bifurcation and pattern formation in a coupled higher autocatalator reaction diffusion system

  • Zhang Li  (张丽)
  • Liu San-yang  (刘三阳)Email author
Article

Abstract

Spatiotemporal structures arising in two identical cells, which are governed by higher autocatalator kinetics and coupled via diffusive interchange of autocatalyst, are discussed. The stability of the unique homogeneous steady state is obtained by the linearized theory. A necessary condition for bifurcations in spatially non-uniform solutions in uncoupled and coupled systems is given. Further information about Turing pattern solutions near bifurcation points is obtained by weakly nonlinear theory. Finally, the stability of equilibrium points of the amplitude equation is discussed by weakly nonlinear theory, with the bifurcation branches of the weakly coupled system.

Key words

reaction diffusion system stability bifurcation pattern 

Chinese Library Classification

O175.29 

2000 Mathematics Subject Classification

35K57 35K55 

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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Zhang Li  (张丽)
    • 1
  • Liu San-yang  (刘三阳)
    • 1
    Email author
  1. 1.Department of Applied MathematicsXidian UniversityXi’anChina

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