A Class of Piecewise Linear Differential Equations Arising in Biological Models
Résumé
We investigate the properties of the solutions of a class of piecewise-linear differential equations. The equations are appropriate to model biological systems in which there are switch-like interactions between the elements of the network. The analysis uses the concept of Filippov solutions of discontinuous righthand sides equations. It gives an insight on the so-called singular solutions which lie on the surfaces of discontinuity. We study several examples of genetic networks.