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SUMMARY:Positive equilibria of weakly reversible power law kinetic systems
with linear independent interactions
DTSTART;VALUE=DATE-TIME:20180711T053000Z
DTEND;VALUE=DATE-TIME:20180711T060000Z
DTSTAMP;VALUE=DATE-TIME:20241107T224142Z
UID:indico-contribution-47@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Editha Jose (University of the Philippines Los Banos
)\nIn this talk\, we present our results on power law kinetic systems whos
e kinetic order vectors (which we call “interactions”) are reactant-de
termined (i.e. reactions with the same reactant complex have identical kin
etic order vectors) and are linear independent per linkage class. In parti
cular\, we focus on its subset called PL-TLK systems. Our main result stat
es that any weakly reversible PL-TLK system has a complex balanced equilib
rium. We can consider this result as a “Higher Deficiency Theorem” for
such systems since in our previous work\, we derived analogues of the Def
iciency Zero and the Deficiency One Theorems for mass action kinetics (MAK
) systems for them\, thus covering the “Low Deficiency” case. On the o
ther hand\, our result can also be viewed as a “Weak Reversibility Theor
em” (WRT) in the sense that the statement “any weakly reversible syste
m with a kinetics from the given set has a positive equilibrium” holds.
According to the work of Deng et al. and more recently of Boros\, such a W
RT holds for MAK systems. However\, we show that a WRT does not hold for t
wo proper MAK supersets: the set PL-NIK of non-inhibitory power law kineti
cs (i.e. all kinetic orders are non-negative) and the set PL-FSK of factor
span surjective power law kinetics (i.e. different reactants imply differ
ent interactions).\n\nhttps://conferences.maths.unsw.edu.au/event/2/contri
butions/47/
LOCATION:University of Sydney New Law School/--101
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/47/
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