the system of SDE is:
dx = (a x - b x y)dt + beta (x dW1 - x y dW2), dy = (c x y - d y)dt + beta (x y dW1 - y dW2)
We solve this system with the Milstein's 2 dimensional method.
dx = {(a-1) x + a x^2 + x (x+1)^2} dt + beta x (1+x) dW
dy = {-a x - a x^2 - x (x+1)^2} dt - beta x (1+x) dW
We solve this system with the Milstein's 2 dimensional method.
The bifurcation point of the noisy brusselator depends both on the constant of noise (beta) and the parameter (a).
For example if beta=0 then the bifurcation point is when a=2, but this changes when we have beta=0.4.
In the graphs bellow we see that if we add noise (beta=0.4) to the system then for a=2 we still have an attractor system but this changes around a=2.12.
the more we add to the noise the larger the value of becomes for the bifurcation
