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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...

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Advance Math

The ”Brusselator” is a mathematical model for a class ofoscillating 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 bare 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) anunstable node (iii) a stable spiral (iv) an unstable

spiral (v) a saddle point. (Not all are possible)

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