Phase Portraits of Gene Networks Models
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Natalia Ayupova1, Vladimir Golubyatnikov2, Vyacheslav Gradov3, Liliya Minushkina4
1Lab. of inverse problems of mathematical physics. Sobolev Institute of Mathematics SB RAS, ayupova@math.nsc.ru
2Lab. of inverse problems of mathematical physics. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia, vpgolubyatn@gmail.com
3Mechanical and mathematical department Novosibirsk State University Novosibirsk, Russia, v.gradov@g.nsu.ru
4Mechanical and mathematical department Novosibirsk State University Novosibirsk, Russia, l.minushkina@g.nsu.ru
We investigate geometric and combinatorial structures of phase portraits of dynamical systems considered as models of functioning of some circular gene networks. Invariant 2-dimensional piecewise linear surfaces constructed here allow to give full description of phase portraits of these models and to control their trajectories