BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nicola Vassena (Leipzig University) DTSTART:20251009T153000Z DTEND:20251009T160000Z DTSTAMP:20260421T124518Z UID:MoRN/131 DESCRIPTION:Title: I nstability and Oscillations in Reaction Networks\nby Nicola Vassena (L eipzig University) as part of Seminar on the Mathematics of Reaction Netwo rks\n\n\nAbstract\nIn the past two decades\, much mathematical research on reaction \nnetworks has focused on multistationarity\, both under mass-ac tion and \nmore general kinetics. Multistationarity typically arises in pa rameter \nspace when a stable steady state loses stability through a real- zero \neigenvalue crossing. More recently\, attention has turned also to \ nstability loss via purely imaginary eigenvalues (Hopf bifurcation)\, \nwh ich is associated with periodic oscillations.\n\nIn this talk\, based on e stablished results from dynamical systems \ntheory developed in late 1970s and 1980s\, I will first clarify that \nfor monostationary networks\, in essence\, any loss of stability \nnecessarily leads to oscillations. I wil l then present sufficient \nconditions for oscillations expressed as algeb raic criteria (for \nmass-action kinetics) and as minimal network motifs ( for general \nkinetics). In turn\, excluding Hopf bifurcations in monostat ionary \nnetworks with a stable steady state is equivalent to 'universal ’ \nstability\, meaning that the unique steady state is locally stable f or \nall parameter choices. I will conclude with a conjecture \ncharacteri zing universal stability for reaction networks with general \nkinetics. Th is is ongoing joint work with Peter F. Stadler and Alex \nBlokhuis.\n LOCATION:https://researchseminars.org/talk/MoRN/131/ END:VEVENT END:VCALENDAR