The 'Brusselator' reaction mechanism proposed in 1968 is schematically represented as A k, X, B+x ,...
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The 'Brusselator' reaction mechanism proposed in 1968 is schematically represented as A k, X, B+x , Y + D, (1) 2X +Y , 3X, X , E, where k;, i = 1,2, 3, 4 are the constant parameters for the rates of reaction, and the reactants A and B are kept constant. du = 1 (b+ 1)u + au?v, dT dv (2) = bu – au'v, dT  where u and v correspond to a = [X] and y = [Y], T = kat %3D (c) Determine the steady states of system (2). (20 Marks) (d) Perform the linear stability analysis of system (2) and show that there is a bifurcation (i.e. change in the stability properties of the steady state) at a point b = b. = 1+ a. (20 Marks) The 'Brusselator' reaction mechanism proposed in 1968 is schematically represented as A k, X, B+x , Y + D, (1) 2X +Y , 3X, X , E, where k;, i = 1,2, 3, 4 are the constant parameters for the rates of reaction, and the reactants A and B are kept constant. du = 1 (b+ 1)u + au?v, dT dv (2) = bu – au'v, dT  where u and v correspond to a = [X] and y = [Y], T = kat %3D (c) Determine the steady states of system (2). (20 Marks) (d) Perform the linear stability analysis of system (2) and show that there is a bifurcation (i.e. change in the stability properties of the steady state) at a point b = b. = 1+ a. (20 Marks)
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