A reaction of A goes to product B with a rate constant.
B can return to A with another rate constant.
We can solve the kinetics of this problem exactly and find that there is just a steady decrease in the concentration of A. The rate of dissapearance of A with time is This expression is composed of two parts. The first is the depletion of the A concentration to form B with a rate constant and the second the formation of A from B with a rate constant . Using this we may eliminate B from the rate equation, . A solution of this equation is . There are no oscillations present in this expression and a simple two step mechanism will not give rise to chemical oscillations.