Bifurcation and Patterns Formation in a Coupled Higher Autocatalator Reaction Diffusion System

ZHANG Li; LIU Sang-yang

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ZHANG Li, LIU Sang-yang. Bifurcation and Patterns Formation in a Coupled Higher Autocatalator Reaction Diffusion System[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1102-1114.

Citation:

ZHANG Li, LIU Sang-yang. Bifurcation and Patterns Formation in a Coupled Higher Autocatalator Reaction Diffusion System[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1102-1114.

Citation:

ZHANG Li, LIU Sang-yang. Bifurcation and Patterns Formation in a Coupled Higher Autocatalator Reaction Diffusion System[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1102-1114.

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Bifurcation and Patterns Formation in a Coupled Higher Autocatalator Reaction Diffusion System

Department of Applied Mathematics, Xidian University, Xi'an 710071, P. R. China

Received Date: 2006-07-04
Rev Recd Date: 2007-06-27
Publish Date: 2007-09-15

Abstract

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 to spatially nonuniform 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.
- reaction diffusion system,
- stability,
- bifurcation,
- pattern

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References(12)

References

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