Numerical and mathematical modeling of a gene network with non-linear degradation of components
V.P. Golubyatnikov, N.E. Kirillova, L.S. Minushkina
Novosibirsk State University, Novosibirsk, Russia
Keywords: non-linear dynamical systems, gene networks models, phase portraits, equilibrium points, invariant domains and toruses, stability, cycles, bifurcations, fast and slow variables, software package STEP
Abstract
For a 3-dimensional dynamical system considered as a model of a gene network with nonlinear degradation of its components, the uniqueness of an equilibrium point is proved. Using approaches of qualitative theory of ordinary differential equations, we find conditions of existence of a cycle of this system and describe an invariant domain which contains all such cycles in the phase portrait. Numerical experiments with trajectories of this system are conducted.
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