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