The Chapman Cycle is a null cycle, meaning that in the net,
nothing really happens (whatever is produced is destroyed). It will produce
a steady-state concentration of O3, because there is both a source and sink
of O3 in the process. Because of the relatively low concentration of gases in
the stratosphere, it takes a relatively long amount of time for each reaction
to take place. This leads to long residence times for each of the reactants
in the Chapman Cycle, which then results in relatively high concentrations of
each of the reactants.
The first two reactions serve as a source of O3. The second two form the sink of O3, with the photodissociation reaction (O3 + UV) being the most important one.
Certain catalysts will add an O3 destruction reaction,
or an additional sink, which throws off the steady-state condition and causes
the O3 concentration to decrease.