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Markov property and chemical oscillators

  1. Sep 17, 2012 #1
    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.


  2. jcsd
  3. Sep 18, 2012 #2


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    Staff: Mentor

    "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.
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