A + B <-> C + D
Taking advantage of 3 algebraic constraints, we reduced our model to a single 1D ODE. The fact that the dynamics is described by a single ODE severely restricts the variety of dynamics that can occur in this system: (see HW#6 solutions!)
In this particular ODE, the outcomes are even more limited. (a) Describe all the qualitatively distinct behaviors that can occur, carefully justifying how you rule out other possibilities. Then specifying what relations among the various parameters (initial concentrations a0, b0, c0, d0, and the forward and backward rate constants, kf and km) determine which kind of behavior occurs.
(b) Generate a quantitively acccurate plot of the concentrations of the 4 species as time goes by: for one set of parameter values and initial conditions of your choice. (Solve the ODE analytically.) Please do not select a constant solution!