Geometric problems of modeling gene networks

00:00 02-12-2007

 

We study 3-dimensional nonlinear dynamical systems of special type as models of simple gene network.

For the gene networks regulated by negative feedbacks, we find sufficient conditions of existence and stability of periodic trajectories.

Here, each of considered dynamical systems has a unique stationary point.

The bifurcation cycles of these systems are described as well.

For the gene networks models of the Glass-Mackey type, we find conditions of existence of 8 stationary points. Here, in some numerical experiments, we have observed 4 periodic trajectories which turn around stationary points with negative topological indices.

 

Joint work with Yurii Gaidov, Novosibirsk State University, Novosibirsk, Russia

 

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