Jacques Belair - Tores invariants et bistabilité de solutions périodiques dans un système d'équations différentielles à retards

The construction of normal forms has been shown to be applicable to systems of delay-differential equations to analyse degenerate (codimension higher than one) bifurcations of stationary solutions. In most instances, this investigation can only be performed using a computer-assisted approach.

We present a model of the insulin-glucose regulatory system for which this technique has been recently applied to show the presence of complicated oscillations, in the form of invariant tori and simultaneous existence of two stable periodic solutions. This system takes the form of two differential equations containing two time delays. The different feedback interactions between the components are quantitatively estimated using data from the clinical literature.

Joint work with Vincent Lemaire; supported by NSERC and FCAR.