Simplified Theory for Time Dynamics of the Period of the B-Z Reaction:
The Bouncing Ball
The partially elastic collisions of a bouncing ball results in each rebound velocity being some constant fraction of the impact velocity. The impact velocity is the same as the previous rebound velocity. This fraction will be called α.
The time of one bounce (the period) is twice one half of the bounce, excluding the time from release to first impact.
And so, the total time is
However, the initial drop is not measured, so
And, since 
†
This equation gives us the time at which the reaction will die.
Now, the time for n periods would be
And, since 
†
Note that:
where t0 corresponds to an imaginary initial period existing before the first bounce.
We can now define a series of period measurement points:
These points can be observed as being points along a single straight line.
Figure 1: A set of points generated by the bouncing-ball theory.
The slope of this line is
The results of this is that measurements of a
bouncing-ball-type phenomenon will follow a straight line on a period vs. time
graph. The y-intercept of this
line will be 
, which is merely some constant representing a combination of
the initial energy of the system and the initial forces acting upon the
system. The slope of the line is a
function of α, the percent of the velocity of the system that is retained each
period.
We can relate this to the percent of energy that is dissipated each period.
