Consider the system of nonlinear chemical reaction A, X, B+Xk2, Y + D, 2X+Y 3X, X4,...

 

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Consider the system of nonlinear chemical reaction A¹, X, B+Xk2, Y + D, 2X+Y 3X, X4, C, where ks are the rate constants, and the reactant concentrations of chemical species A and B are kept at constant values of a and b, respectively, for all time. (a) Write the governing differential equation system, according to the law of mass ac- tion, for the concentrations of X and Y; nondimensionalize the equation so that they be- comes du Bu-au²v, dT in which u and u are the corresponding variables for the concentrations of X and Y, T = kat, a = (k₁a)²ks/ki, and 3= k₂b/ks. = (b) Determine the positive steady state and show that there is a bifurcation value Be= 1+ a at which the steady state becomes unstable in a Hopf bifurcation way. (c) Show that in the vincinty of B = Be, the limit cycle has a period of 2π/√a. find A,B,C,D SOLVE using R language = 1-(8+1)u+au²v, dv dr = Consider the system of nonlinear chemical reaction A¹, X, B+Xk2, Y + D, 2X+Y 3X, X4, C, where ks are the rate constants, and the reactant concentrations of chemical species A and B are kept at constant values of a and b, respectively, for all time. (a) Write the governing differential equation system, according to the law of mass ac- tion, for the concentrations of X and Y; nondimensionalize the equation so that they be- comes du Bu-au²v, dT in which u and u are the corresponding variables for the concentrations of X and Y, T = kat, a = (k₁a)²ks/ki, and 3= k₂b/ks. = (b) Determine the positive steady state and show that there is a bifurcation value Be= 1+ a at which the steady state becomes unstable in a Hopf bifurcation way. (c) Show that in the vincinty of B = Be, the limit cycle has a period of 2π/√a. find A,B,C,D SOLVE using R language = 1-(8+1)u+au²v, dv dr =

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Solution Given that ka X ... View the full answer