For the Brusselator model with parameter

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems

Many Parts, One Behaviour, Ch Pattern formation: instabilities that choose a wavelength

Problem

A = 1.5

, diffusion coefficients

D_u = 1

and

D_v = 6

(dimensionless model units), the Hopf threshold is

B_{\rm H} = 1+A^2

, the Turing threshold is

B_{\rm T} = (1+A\sqrt{D_u/D_v})^2

, and the critical wavenumber satisfies

q_{\rm c}^2 = A/\sqrt{D_uD_v}

. ((a)) Compute

B_{\rm H}

and

B_{\rm T}

and say which instability occurs first as

B

is raised from zero. ((b)) Compute the critical wavenumber

q_{\rm c}

and the pattern wavelength

\Lambda_{\rm c} = 2\pi/q_{\rm c}

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