Affiliations: [a] Institute for Mathematics, Free University of Berlin, Berlin, Germany | [b] Peoples’ Friendship University of Russia, Moscow, Russia. E-mail: gurevich@math.fu-berlin.de | [c] Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, TX, USA. E-mail: dmitry.rachinskiy@utdallas.edu
Correspondence:
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Corresponding author: Dmitrii Rachinskii, Department of Mathematical Sciences, The University of Texas at Dallas, 800 West Campbell Road, Richardson, TX 75080-3021, USA. Tel.: +1 972 883 4401; Fax: +1 972 883 6622; E-mail: dmitry.rachinskiy@utdallas.edu.
Abstract: 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.
