A model for two chemicals that inhibit one another is x\' = 0.5n/0.5n + yn -x y\

Question

A model for two chemicals that inhibit one another is x' = 0.5n/0.5n + yn -x y' = 0.5n/0.5n + xn -y where n is a positive number. There is one steady state with x - y, find it. Show that the equilibrium is stable if n 2. What happens to the system when the equilibrium point becomes unstable? The ''Brusselator'' is a mathematical model for a class of oscillating chemical reactions x' = 1 - (b + l)x + ax2y y' = bx - ax2y where x, y 0 are the concentrations of the chemical and a and b are positive constants Find the value of x and y at the equilibrium point. 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)

Explanation / Answer

(a) with f(x) = 0.5.e^x - x

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