hopf bifurcation for brusselator

Hello everyone!

I have a question about hopf bifurcation for a brusselator problem, how to

implement a code for that. For now my code that I have written looks like below:

a = 1;
b = 2;

x0 = [0 5];

tspan = [1,100];

Bruss = @(t,x) [1 - (b+1)*x(1) + a*x(1)^2*x(2); b*x(1) - a*x(1)^2*x(2)];

options = odeset('RelTol',1e-6,'AbsTol',1e-4);

[T,x] = ode45(Bruss,tspan,x0,options);

% x1 = linspace(0,100,5000);
x1 = x(:,1);
y1 = x(:,2);
% y1 = linspace(0,100,5000);
xnully = ((b+1).*x1-1)./(a.*x1.^2);
ynully = b./(a.*y1);
 
plot(x1,xnully,y1,ynully);
axis([0 4 0 4])
hold on

% plot(T,x(:,2),T,x(:,1))
% hold on
% plot(a,b/a,'r')

% [m,n] = size(x) ;
[x2,y2] = meshgrid(0:.2:4,0:.2:4);
U = 1-(b+1).*x2 + a.*y2.*x2.^2;
V = b.*x2 - a.*y2.*x2.^2;
L = sqrt(U.^2 + V.^2);
quiver(x2,y2,U./L,V./L,.5,'k')
hold on
plot(a,b/a,'r*')

[Ana Sar]

Hello!

Have you found a solution for this problem? If the answer is yes, please please share it here.