Avalanche of Bifurcations and Hysteresis in a Model of Cellular Differentiation

Details Avalanche of Bifurcations and Hysteresis in a Model of Cellular Differentiation Avalanche of Bifurcations and Hysteresis in a Model of Cellular Differentiation

2003-09-16

arxiv.org/abs/nlin/0309046v1

Physical Review E 60 (4), 4604 (1999)

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

10.1103/PhysRevE.60.4604

Cellular differentiation in a developping organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emenating 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 cells change type up to a given distance, or under other conditions, the differentiation process propagates through the whole domain. When the signal diminishes hysteresis is observed.

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