Asymptotics of sign-changing patterns in hysteretic systems with diffusive thresholds

摘要

We consider a reaction-diffusion system including discontinuous hystereticrelay operators in reaction terms. This system is motivated by an epigeneticmodel that describes the evolution of a population of organisms which canswitch their phenotype in response to changes of the state of the environment.The model exhibits formation of patterns in the space of distributions of thephenotypes over the range of admissible switching strategies. We proposeasymptotic formulas for the pattern and the process of its formation.