clear

nu=0.5;
Omega=1;
kappa=0.001;
dt=0.001;
endt=2*pi*10;

Nt=floor(endt/dt)+1
x=zeros(Nt,1);
y=x;
t=x;
x(1)=2;
y(1)=0;
t(1)=0;
tic
r=randn(Nt,2);
for n=1:(Nt-1)
    x(n+1)=x(n)+dt*(nu*(1-x(n)^2-y(n)^2)*x(n)-Omega*y(n))+sqrt(2*kappa*dt)*r(n,1);
    y(n+1)=y(n)+dt*(nu*(1-x(n)^2-y(n)^2)*y(n)+Omega*x(n))+sqrt(2*kappa*dt)*r(n,2);
    t(n+1)=t(n)+dt;
end

figure
plot(x,y,'b-')
toc