Homework Solution: The Schlogl model is famous for its bistable steady-state distribution. The reactions are B_1 2X rightwardsharpo…

    3. Schlögl model. The Schlögl model is famous for its bistable steady-state distri- bution. The reactions are where Bi and B2 denote buffered species whose respective molecular populations Ni and N2 are assumed to remain essentially constant over the time interval of interest. There is only one time-varying species, X; the state change vectors are v, = V3 = 1, ½ = Va =-1; and the propensity functions are al (x) a2(x) 우Nix(x-1) 똥x(x-1)(x-2). = = a4(x) = car For some values of the parameters this model has two stable states, and that is the case for the parameter values we have chosen here: 3 × 10-7. C3 = 10-3, №=2x105 c; C2 = 10-4, c-3.5. Ni=1x105, In the following questions, we assume the initial condition is at X(0) 250. (a) Write down the Chemical Master Equation for the model. (b) Write down the reaction rate equations and simulate the equation in matlab. (c) Write a program to run the SSA simulation and compare the result with the reaction rate equations result. You need to show at least five different trajectories.

    The Schlogl model is famous for its bistable steady-state distribution. The reactions are B_1 2X rightwardsharpoonoverleftwardsharpoon 3X, B_2 rightwardsharpoonoverleftwardsharpoon X, where B_1 and B_2 denote buffered species whose respective molecular populations N_1 and N_2 are assumed to remain essentially constant over the time interval of interest. There is only one time-varying species, X: the state change vectors are v_1 = V_3 = 1, v_2 = V_4 = -1: and the propensity functions are a_1(x) = c_1/2 N_1x(x - 1), a_2(x) = c_2/6x(x - 1)(x - 2) a_3(x) = c_3N_2, a_4(x) = c_4x. For some values of the parameters this model has two stable states, and that is the case for the parameter values we have chosen here: c_1 = 3 times 10^-7, c_2 = 10^-4, c_3 = 10^-3, c_4 = 3.5, N_1 = 1 times 10^5, N_2 = 2 times 10^5. In the following questions, we assume the initial condition is at X(0) = 250. (a) Write down the Chemical Master Equation for the model. (b) Write down the reaction rate equations and simulate the equation in matlab. (c) Write a program to run the SSA simulation and compare the result with the reaction rate equations result. You need to show at least five different trajectories.

    Expert Answer

    3. Schlögl design. The Schlögl design is illustrious ce its bidurable steady-specify distri- bution. The reactions are where Bi and B2 propound buffered figure whose appertaining molecular populations Ni and N2 are conjectured to rest essentially uniform balance the season period of cause. There is simply undivided season-varying figure, X; the specify vary vectors are v, = V3 = 1, ½ = Va =-1; and the proclivity functions are al (x) a2(x) 우Nix(x-1) 똥x(x-1)(x-2). = = a4(x) = car Ce some values of the parameters this design has brace durable specifys, and that is the plight ce the parameter values we accept selected here: 3 × 10-7. C3 = 10-3, №=2x105 c; C2 = 10-4, c-3.5. Ni=1x105, In the aftercited questions, we exhibit the primal proviso is at X(0) 250. (a) Write down the Chemical Master Equation ce the design. (b) Write down the reaction trounce equations and presume the equation in matlab. (c) Write a program to fly the SSA euphuism and assimilate the fruit with the reaction trounce equations fruit. You want to pretext at meanest five opposed trajectories.

    The Schlogl design is illustrious ce its bidurable steady-specify classification. The reactions are B_1 2X rightwardsharpoonoverleftwardsharpoon 3X, B_2 rightwardsharpoonoverleftwardsharpoon X, where B_1 and B_2 propound buffered figure whose appertaining molecular populations N_1 and N_2 are conjectured to rest essentially uniform balance the season period of cause. There is simply undivided season-varying figure, X: the specify vary vectors are v_1 = V_3 = 1, v_2 = V_4 = -1: and the proclivity functions are a_1(x) = c_1/2 N_1x(x – 1), a_2(x) = c_2/6x(x – 1)(x – 2) a_3(x) = c_3N_2, a_4(x) = c_4x. Ce some values of the parameters this design has brace durable specifys, and that is the plight ce the parameter values we accept selected here: c_1 = 3 seasons 10^-7, c_2 = 10^-4, c_3 = 10^-3, c_4 = 3.5, N_1 = 1 seasons 10^5, N_2 = 2 seasons 10^5. In the aftercited questions, we exhibit the primal proviso is at X(0) = 250. (a) Write down the Chemical Master Equation ce the design. (b) Write down the reaction trounce equations and presume the equation in matlab. (c) Write a program to fly the SSA euphuism and assimilate the fruit with the reaction trounce equations fruit. You want to pretext at meanest five opposed trajectories.

    Expert Repartee

     

    ** Plea