  We introduce a mathematical model of savanna vegetation dynamics. The usual
approach of nonequilibrium ecology is extended by including the impact of wet
and dry seasons. We present and rigorously analyze a model describing a mixed
woodland-grassland ecosystem with stochastic environmental noise in the form of
vegetation biomass losses manifesting fires. Both, the probability of ignition
and the strength of these losses depend on the current season (as well as
vegetation growth rates etc.). Formally it requires an introduction and
analysis of a system that is a piecewise deterministic Markov process with
parameters switching between given constant periods of time. We study the long
time behavior of time averages for such processes.
