Remarks on pattern formation in a model for hair follicle spacing
Peter Rashkov
Discrete & Continuous Dynamical Systems - B 2015, 20(5): 1555-1572 doi: 10.3934/dcdsb.2015.20.1555
A modified version of the Gierer-Meinhardt reaction-diffusion system (without source terms) is used in a model for hair follicle spacing in mice, proposed by Sick, Reinker, Timmer and Schlake [22]. Global existence of solutions of this model system is shown by computing uniform bounds. Analysis of conditions for emergence of spatially heterogeneous solutions is performed using a limiting form of the original reaction-diffusion system. The conditions for pattern formation given in [22] are improved by including those subregions in the parameter space where far-from-equilibrium heterogeneous solutions occur.
keywords: pattern formation Biological modelling far-from-equilibrium solutions. Turing instability dynamical systems

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