Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Ruling out Hopf bifurcations in biochemical reaction networks
Casian Pantea

Last modified: 2014-06-09


We describe a new graphical approach to the question of whether dynamical systems modeling networks of interacting elements admit Hopf bifurcations. The techniques make use of the spectral properties of additive compound matrices: in particular, we show that a condition on the cycles of a labelled digraph (called the DSR[2] graph) rules out the possibility of nonreal eigenvalues of the Jacobian matrix passing through the imaginary axis.