  We consider a reaction-diffusion system including discontinuous hysteretic
relay operators in reaction terms. This system is motivated by an epigenetic
model that describes the evolution of a population of organisms which can
switch their phenotype in response to changes of the state of the environment.
The model exhibits formation of patterns in the space of distributions of the
phenotypes over the range of admissible switching strategies. We propose
asymptotic formulas for the pattern and the process of its formation.
