Hierarchical analysis of piecewise affine models of gene regulatory networks

We propose in this report a method for the qualitative analysis of the dynamics of piecewise affine models of gene regulatory networks. Especially adapted to the framework of piecewise affine dynamical systems, this method is based on the hierarchical organization of such systems, using the well-known algorithm of decomposition of the interaction graph into strongly connected components. In certain cases, this decomposition allows to reduce the study of the asymptotic dynamics of a high dimensional system into the one of several lower dimensional subsystems. Allied to a threshold elimination algorithm as a pre-processing treatment, this method is applied to a $9$-dimensional system modeling the nutritional stress response of the bacterium \textit{E. coli}. In this case, we manage to reduce the analysis of the whole system to the analysis of a $3$-dimensional subsystem

Hierarchical analysis of piecewise affine models of gene regulatory networks

We propose in this report a method for the qualitative analysis of the dynamics of piecewise affine models of gene regulatory networks. Especially adapted to the framework of piecewise affine dynamical systems, this method is based on the hierarchical organization of such systems, using the well-known algorithm of decomposition of the interaction graph into strongly connected components. In certain cases, this decomposition allows to reduce the study of the asymptotic dynamics of a high dimensional system into the one of several lower dimensional subsystems. Allied to a threshold elimination algorithm as a pre-processing treatment, this method is applied to a $9$-dimensional system modeling the nutritional stress response of the bacterium \textit{E. coli}. In this case, we manage to reduce the analysis of the whole system to the analysis of a $3$-dimensional subsystem