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Avalanche of bifurcations and hysteresis in a model of cellular differentiation
1Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, England.
Abstract:
Cellular differentiation in a developing organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emanating from its environment. Depending on the form of the nonlinear reaction kinetics, this signal can trigger a series of bifurcations in the system. Differentiation starts at the surface where the signal is received and either cells change type up to a given distance or, under other conditions, the differentiation process propagates throughout the whole domain. When the signal diminishes, hysteresis is observed.
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