In: Advanced Math
The ”Brusselator” is a mathematical model for a class of oscillating chemical reactions
x'= 1−(b+ 1)x+a(x^2)y
y′= bx−a(x^2)y
where x,y ≥ 0 are the concentrations of the chemical and a and b are positive constants
(a) Find the value of x and y at the equilibrium point.
(b) Find values of a and b that give (i) a stable node (ii) an unstable node (iii) a stable spiral (iv) an unstable
spiral (v) a saddle point. (Not all are possible)