Markov property and chemical oscillators

[cjolley]

Hi everybody...

I've been working a bit with models of chemical oscillators and I've run into something that isn't quite clear to me.

Chemical reaction systems are typically regarded as having the Markov property -- they lack memory and their evolution depends only on their current state. Under a not-too-restrictive set of conditions, Markov chains will have a stationary distribution: the basic requirement seems to be that any state be reachable from any other in a finite number of steps. This seems like something that will generally be true for chemical systems, at least on the lattice of stoichiometrically-compatible states.

Here's where this starts to bother me: it's also fairly easy to set up a Monte Carlo simulation of a chemical reaction system that shows bulk oscillations. Do chemical oscillators somehow violate the conditions required for Markov chain stationarity? Or am I comparing apples and oranges here? This seems like a reasonable question, but an hour or so of poking around on the internet has turned up nothing directly relevant.

Thanks!

--craig

 

[mfb]

"There is a stationary distribution" and "everything will approach a stationary distribution" are two completely different things. In addition, I think even those chemical oscillators will approach an equilibrium after a while.