Singularly impulsive mathematical model of Delta — Notch signaling system

Abstract

In this paper we present mathematical model of well known Delta-Notch signaling system in form of nonlinear, singular, impulsive and singularly impulsive dynamical systems. This example is interesting since it posses phenomena of lateral inhibition recognized to be underlying element in mechanism structures in many living organisms. It is characterized by beautiful patterns as a result of singling out of one cell for one particular cell fate, while neighboring cells are determined for secondary, different cell fate. Topic is very interesting for rising scientific questions and reasons why it happens and how, it is interesting for pattern formation in engineering, and is also very attractive topic in mathematics.