Parameter estimation and Stability of equilibrium of Gene Regulatory Network by Piecewise Multi-affine approach

In this paper, we developed a new method to estimate parameter area and analyze the stability of equilibrium for gene regulatory network by piecewise multi-affine (PMA) approach. For the PMA function, it is continuous and the thresholds of its partition the phase space into many subspace. In every subspace, the model can be transformed into linear model, so the stable and unstable manifolds of equilibrium points can be determined analytically and stability and bifurcation can be obtained easily and the corresponding parameter areas can be obtained. This method allows us to estimate and tune parameter for a kind of high dimensional gene network and analyze the dynamical behaviors of its. In the end, Repressilator model, as an example, illustrates the validity of the method in this paper.