Amplified Hopf Bifurcations in Feed-Forward Networks

Amplified Hopf Bifurcations in Feed-Forward Networks

In [18] the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter families of homogeneous feed-forward chains with 2-dimensional cells. Our main result is that Hopf bifurcations in such families generically generate branches of periodic solutions with amplitudes growing like ∼ |λ| 1 2 ,∼ |λ| 1 ...

Protection from Feed-Forward Amplification in an Amplified RNAi Mechanism

The effectiveness of RNA interference (RNAi) in many organisms is potentiated through the signal-amplifying activity of a targeted RNA-directed RNA polymerase (RdRP) system that can convert a small population of exogenously-encountered dsRNA fragments into an abundant internal pool of small interfering RNA (siRNA). As for any biological amplification system, we expect an underlying architecture...

Computing Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates

The analysis of dynamic of chemical reaction networks by computing Hopf bifurcation is a method to understand the qualitative behavior of the network due to its relation to the existence of oscillations. For low dimensional reaction systems without additional constraints Hopf bifurcation can be computed by reducing the question of its occurrence to quantifier elimination problems on real closed...

Discretizing Dynamical Systems with Hopf-Hopf Bifurcations

We consider parameter-dependent, continuous-time dynamical systems under discretizations. It is shown that Hopf-Hopf bifurcations are O(h)-shifted and turned into double Neimark-Sacker points by general one-step methods of order p. Then we discuss the effect of discretization methods on the emanating Hopf curves. The numerical approximation of the critical eigenvalues is analyzed too. The resul...

Double Hopf Bifurcations