Applied Math Seminar
Spring Quarter 2008
3:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-C

Friday, April 4, 2008

Vladimir Golubyatnikov
Sobolev Institute of Mathematics
Novosibirsk, Russia

Existence and stability of closed cycles
in nonlinear dynamical systems of kinetic type


Abstract:

We study models of functioning of Gene Networks and their phase portraits, in particular, we describe stationary regimes and bifurcations of closed cycles in corresponding dynamical systems.

For some types of the Gene Networks with negative feedback regulation mechanisms, we prove existence of non-bifurcation cycles and obtain estimates of stability of these periodic trajectories.

We consider here the Gene Networks models with combinations of positive and negative feedbacks as well, in particular, we study the phase portraits of the Glass-Mackey type dynamical systems.