Hans G Kaper et al 2009 Nonlinearity 22 601 doi:10.1088/0951-7715/22/3/006
Hans G Kaper1,3, Shouhong Wang2 and Masoud Yari2
Show affiliationsRecommended by J A Glazier
This paper is concerned with the formation and persistence of spatiotemporal patterns in binary mixtures of chemically reacting species, where one of the species is an activator, the other an inhibitor of the chemical reaction. The system of reaction–diffusion equations is reduced to a finite system of ordinary differential equations by a variant of the centre-manifold reduction method. The reduced system fully describes the local dynamics of the original system near transition points at the onset of instability. The attractor–bifurcation theory is used to give a complete characterization of the bifurcated objects in terms of the physical parameters of the problem. The results are illustrated for the Schnakenberg model.
82.40.Np Temporal and spatial patterns in surface reactions
82.40.Bj Oscillations, chaos, and bifurcations
82.20.-w Chemical kinetics and dynamics
05.45.-a Nonlinear dynamics and nonlinear dynamical systems
82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer
35K57 Reaction-diffusion equations
Issue 3 (March 2009)
Received 19 November 2008, in final form 19 January 2009
Published 10 February 2009
Hans G Kaper et al 2009 Nonlinearity 22 601
Mark Braverman 2006 Nonlinearity 19 1383
M Hairer 2002 Nonlinearity 15 271
Henk Broer et al 2002 Nonlinearity 15 1205
J-P Eckmann and M Hairer 2001 Nonlinearity 14 133
H W Broer et al 1998 Nonlinearity 11 1569
Maximilian Amsler et al 2009 Nanotechnology 20 445301
Kjetil Gjerde et al 2006 Nanotechnology 17 4917
Patrick L T M Frederix et al 2005 Nanotechnology 16 997
X H Ji et al 2005 Nanotechnology 16 3069