Stochastic Brusselator Simulation

on 6 Oct 2022

% 2-D Stochastic Brusselator dynamics simulation

% Based on brusselator2_sde_milstein.m demo in my SDETools toolbox:

% https://mathworks.com/matlabcentral/fileexchange/56406

dt=5e-2; % Integration time step

n=64; % Dimension of the 2-D spatial grid

a=1; % Reaction constant

b=3; % Reaction constant

u=0.2; % Drift coefficient

v=0.02; % Drift coefficient

s=5e-2; % Noise magnitude

k=[0 1 0;

1 -4 1;

0 1 0]/4; % Laplacian convolution kernel

rng(1); % Set random seed

y=2*rand(n,n,2); % State matrices with random initial conditions

% Mask for borders

m=0*y;

m(2:n-1,2:n-1,:)=1;

for i=1:2e4 % Integration steps

X=y(:,:,1);

Y=y(:,:,2);

% 2-D Brusselator drift function using convolution

B=(b-Y.*X).*X;

f=cat(3,a-B-X+u*conv2(X,k,'s'),B+v*conv2(Y,k,'s'));

% 2-D Brusselator diffusion function

g=s*cat(3,-X,X);

% Euler-Maruyama integration of the SDE

y=y+m.*(f*dt+g*sqrt(dt).*randn(n,n,2));

end

imshow(y(:,:,1),[],'C',parula) % Scale and apply colormap