Mathematical and Numerical Modeling of the Pluripotency Gene Network Dynamics

We consider nonlinear dynamical systems as models of interaction of components of a gene network which regulates early stages of an embryonic stem cells state. A parametric analysis of these dynamical systems is performed in order to describe the (non)uniqueness and stability of their equilibriums. We have obtained a criterion of existence of periodic trajectories near these points and localized such oscillations on the phase portraits of dynamical systems which describe these processes. A special software for cloud numerical experiments with such systems has been elaborated.