Mathematical and numerical modeling of the pluripotency gene network dynamics
V.P. Golubyatnikov, E. A. Tatarinova
Novosibirsk State University, Novosibirsk, Russia
Keywords: gene networks, positive and negative feedbacks, nonlinear dynamical systems, equilibrium points, stability
Abstract
We consider nonlinear dynamical systems as a model 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 these oscillations on the phase portraits of dynamical systems which describe these processes. A special software for cloud numerical experiments with these systems has been elaborated.
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