Hopf Bifurcations of Reaction Networks with Zero-One Stoichiometric Coefficients

Időpont: 
2022. 09. 13. 17:00
Hely: 
Google Meet
Előadó: 
Xiaoxian Tang

 Xiaoxian Tang, K Wang: 

Hopf Bifurcations of Reaction Networks with Zero-One Stoichiometric Coefficients

For the reaction networks with zero-one stoichiometric coefficients (or simply zero-one networks), we prove that if a network admits a Hopf bifurcation, then the rank of the stoichiometric matrix is at least four. As a corollary, we show that if a zero-one network admits a Hopf bifurcation, then it contains at least four species and five reactions. As applications, we show that there exist rank-four subnetworks, which have the capacity for Hopf bifurcations/oscillations, in two biologically significant networks: the MAPK cascades and the ERK network. We provide a computational tool for computing all four-species, five-reaction, zero-one networks that have the capacity for Hopf bifurcations.

Google meet link:  https://meet.google.com/bgt-oqys-gme