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Monday, April 16, 2012
3:00 PM - 4:00 PM
CNLS Conference Room (TA-3, Bldg 1690)

Colloquium

Stability and Instability in Chemical Reaction Networks: The Big Picture

Martin Feinberg
Ohio State University

In nature there are millions of distinct networks of chemical reactions that might present themselves for study at one time or another. Written at the level of elementary reactions taken with classical mass action kinetics, each new network gives rise to its own (usually large) system of polynomial equations for the species concentrations. Polynomial systems in general, even simple ones, are known to be rich sources of interesting and sometimes wild dynamical behavior. It would appear, then, that chemistry too should be a rich source of dynamical exotica. Yet there is a remarkable amount of stability in chemistry. Indeed, chemical engineers generally expect homogeneous isothermal reactors, even highly complex ones, to behave in quite dull ways. Alt-hough this tacit doctrine of stable behavior is supported by a long observational record, there are certainly instances of homogeneous isothermal reactors that give rise, for example, to bistability or even chaotic behavior. The vast landscape of chemical reaction networks, then, appears to have wide regions of intrin-sic stability (regardless of parameter values) punctuated by smaller regions in which instability might be extant (for at least certain parameter values). I will present some work (with George Craciun, Phillipp Ellison, and Guy Shinar) that goes a long way toward explaining this landscape in particular, toward explaining how biological chemistry, governed by the same rules as all of chemistry, nevertheless "escapes" the stability doctrine to make life interesting.

Host: Mike Wall, CNLS, mewall@lanl.gov