Hybrid reaction-diffusion and clock-and-wavefront model for the arrest of oscillations in the somitogenesis segmentation clock.

The clock and wavefront paradigm is arguably the most widely accepted model for explaining the embryonic process of somitogenesis. According to this model, somitogenesis is based upon the interaction between a genetic oscillator, known as segmentation clock, and a differentiation wavefront, which provides the positional information indicating where each pair of somites is formed. Shortly after the clock and wavefront paradigm was introduced, Meinhardt presented a conceptually different mathematical model for morphogenesis in general, and somitogenesis in particular.

Searching for spatial patterns in a pollinator-plant-herbivore mathematical model.

This paper deals with the spatio-temporal dynamics of a pollinator-plant-herbivore mathematical model. The full model consists of three nonlinear reaction-diffusion-advection equations defined on a rectangular region. In view of analyzing the full model, we firstly consider the temporal dynamics of three homogeneous cases.