  We investigate the sensitivity of the time evolution of a kinetic Ising model
with Glauber dynamics against the initial conditions. To do so we apply the
"damage spreading" method, i.e., we study the simultaneous evolution of two
identical systems subjected to the same thermal noise. We derive a master
equation for the joint probability distribution of the two systems. We then
solve this master equation within an effective-field approximation which goes
beyond the usual mean-field approximation by retaining the fluctuations though
in a quite simplistic manner. The resulting effective-field theory is applied
to different physical situations. It is used to analyze the fixed points of the
master equation and their stability and to identify regular and chaotic phases
of the Glauber Ising model. We also discuss the relation of our results to
directed percolation.
